Correct answer is $\mathrm{v}$ Explanation: We know the formula of force experienced by a moving charge in magnetic field : $ \begin{array}{l} \mathrm{F}=\mathrm{q}(\mathrm{v} \times \mathrm{B}) \\...

### A charge ‘ ‘ moving with velocity’ ‘in a magnetic field of induction ‘ , experiences force ‘. The angle between and is . The speed of ‘ after one second will be

### A geyser is rated 1500 W, 250 V. This geyser is connected to 250 V mains. Calculate:

(i)The current drawn,

(ii)The energy consumed in 50 hours, and

(iii)The cost of energy consumed at ₹ 4.20 per kWh.

We know that Geyser power, P = 1500 W , V = 250 V (i) since, Current, I = P / V thus, I = 1500 / 250 I = 6 A (ii) Time, t = 50 h Energy, E = P × t E = 1500 × 50 E = 75000 Wh E = 75 kWh (iii) hence...

### An electric kettle is rated 2.5 kW, 250 V’. Find the cost of running the kettle for two hours at ₹ 5.40 per unit

We know that, kettle power, P = 2.5 kW Potential difference V = 250 V t = 2 h since, Energy, E = P × t E = 2.5 × 2 E = 5 kWh Cost per unit of energy = ₹ 5.40 Cost for 5 kWh of energy = 5.40 × 5 = ₹...

### An electric toaster draws current 8 A in a circuit with source of voltage 220 V. It is used for 2 h. Find the cost of operating the toaster if the cost of electrical energy is ₹ 4.50 per kWh

According to the question, Given that V = 220 V I = 8 A , t = 2 h E = VIt We know that E = 220 × 8 × 2 E = 3520 Wh E = 3.52 kWh Therefore, Cost of 3.52 kWh energy is ₹ 4.50 × 3.52 kWh= ₹...

### Water in an electric kettle connected to a 220 V supply took 5 minutes to reach its boiling point. How long will it take if the supply had been of 200 V?

According to the question, \(P={{V}^{2}}/R\) Heat gained = (\{{V}^{2}}/R\times t\) (V12 / R) × t1 = (V22 / R) × t2 t2 = (V1 / V2)2 × t1 This implies that t2 = 6.05 min.

### A battery of e.m.f. 15 V and internal resistance 2 ohm is connected to two resistors of resistances 4 ohm and 6 ohm joined in series. Find the electrical energy spent per minute in 6 ohm resistor.

According to the question, battery emf V = 15 V RB = 2 ohm (Internal resistance of battery) Resistances given in circuit are 4 ohm and 6 ohm respectively. (i) In series, Equivalent resistance, R =...

### Two resistors A and B of 4 ohm and 6 ohm, respectively are connected in parallel. The combination is connected across a 6 volt battery of negligible resistance. Calculate: (i) the power supplied by the battery, (ii) the power dissipated in each resistor.

Provided, RA = 4 ohm resistance RB = 6 ohm resistance V = 6 V is the voltage. (i)Due to the parallel connection of the resistances 1 / R = 1 / 4 + 1 / 6 1 / R = 10 / 24 R = 2.4 ohm We are aware of...

### A bulb is connected to a battery of p.d. 4 V and internal resistance 2.5 ohm. A steady current of 0.5 A flows through the circuit. Calculate:

(i)The total energy supplied by the battery in 10 minutes,

(ii)The resistance of the bulb, and

(iii)The energy dissipated in the bulb in 10 minutes.

We know that, V = 4 V is the voltage. 2.5 ohm is the battery resistance. I = 0.5 A (current) E = V2t / R (Energy supplied by the battery) t = 10 × 60 t = 600 sec R = V / I R = 4 / 0.5 R = 8 ohm E =...

### Three heaters each rated 250 W, 100 V are connected in parallel to a 100 V supply. Calculate:

(i)The total current taken from the supply,

(ii)The resistance of each heater, and

(iii)The energy supplied in kWh to the three heaters in 5 hours.

Given, P = 250 W V = 100 V is the voltage. I =? (Current flowing through each heater) Because P = VI I = P / V I = 250 / 100 I = 2.5 A ∴ For the three heaters, current was taken. = 3 × 2.5 = 7.5 A...

### An electric bulb is rated 250 W, 230 V.

(i) the energy consumed in one hour, and

(ii) the time in which the bulb will consume 1.0 kWh energy when connected to 230 V mains?

We know that, P = 250 W(Power) V = 230 V(Voltage) (i) E = P × t t = 3600 sec Given that, E = 250 × 3600 E = 9 × 105 J (ii) 1000 Wh = 250 × t Hence, time,=4 hours

### Two bulbs are rated 60 W, 220 V and 60 W, 110 V, respectively. Calculate the ratio of their resistances.

Given, V1 = 220 V voltage 110 volts V2 , P1 = P2 = P = 60 W We are aware of this. V2 / P = R R1 = V12 / P R1 = (220)2 / 60 R2 = V22 / P R2 = (110)2 / 60 Now, if we divide R1 and R2 together, we...

### What is the resistance, under normal working conditions, of an electric lamp rated at ‘240 v’, 60 W? If two such lamps are connected in series across a 240 V mains supply, explain why each one appears less bright.

Given, V Equals 240 V Voltage P = 60 W We are aware of this. P = V2 / R R = V2 / P R = (240)2 / 60 R = 960 ohm I = P / V I = 60 / 240 I = 0.25 A When one lamp is connected across the mains, the...

### A current of 0.2 A flows through a wire whose ends are at a potential difference of 15 V. Calculate:

(i)The resistance of the wire, and

(ii)The heat energy produced in 1 minute.

Given, I = 0.2 A current V = 15 V potential difference t = 60 seconds Because V = IR, (a) Determining the wire's resistance V / I = R R = 0.2 / 15 R = 75 ohm (b) Determine the amount of heat energy...

### A bulb rated 12 V, 24 W operates on a 12 volt battery for 20 minutes. Calculate:

(i) the current flowing through it, and

(ii) the energy consumed.

We know that, P = 24 W (power) V = 12 V is the voltage. I =? We are aware of this. P = VI = Power (i) It has a current running through it. I = 12 / 24 2 A = I (ii) Energy, E = P × t E = 24 × 20 × 60...

### An electrical appliance having a resistance of 200 ohm is operated at 200 V. Calculate the energy consumed by the appliance in 5 minutes (i) in joule, (ii) in kWh

We know that, Resistance = 200 ohm Voltage = 200 V time = 5 minutes As we know, Energy= V2t / R (i) Energy in joules E = [(200)2 × 300] / 200 Hence, E = 60000 J (ii) Energy is In kWh Since1 kWh =...

### An electric press is rated ‘750 W, 230 V’. Calculate the electrical energy consumed by the press in 16 hours

According to the question, P=750W P.D=230 V We know that E = Power × time E = 750 × 16 E = 12000 Wh Hence, E = 12 kWh

### A bulb of power 40 W is used for 12.5 h each day for 30 days. Calculate the electrical energy consumed.

We know E = P t 40 x 12.5 = E 500 Wh = E 30 days of energy use E = 500 x 30 15000 Wh = E 15 kWh = E

### An electric bulb is rated at 220 V, 100 W. (a) What is its resistance? (b) What safe current can be passed through it?

(a) Assume P = 100 W V = 220 V is the voltage. We are aware of this. P = V2 / R = Power R = (220)2 / 100 484 ohm (b) The current that may be safely carried through it is P / V = I I = 220 / 100 0.45...

### An electric bulb is rated ‘100 W, 250 V’. How much current will the bulb draw if connected to a 250 V supply?

We know that, P = 100 W V Equals 250 V Voltage We are aware of this. P = VI = Power P / V = I I = 100 / 250 0.4 A = I

### Calculate the current through a 60 W lamp rated for 250 V. If the line voltage falls to 200 V, how is power consumed by the lamp affected?

We know that, P = 60 W V = 250 V Let us consider, P = VI I = 60 / 250 This implies I = 0.24 A We know Resistance of lamp R = V2 / P R = (250)2 / 60 R = 1041.6 ohm If the voltage drops to 200 V, the...

### A current of 2 A is passed through a coil of resistance 75 Ω for 2 minutes.

(a) How much heat energy is produced?

(b) How much charge is passed through the resistance?

According to the question, Given that (I) = 2 A R = 75 Ω t = 120 s (a)so, Heat produced, H = I2Rt or H = (2)2 (75) (120) J = 36000 J (b) We know that Q = It or Q = (2) (120) C Therefore, Q = 240 C...

### An electric bulb of resistance 500 ohm draws current 0.4 A from the source. Calculate: (a) the power of bulb and (b) the potential difference at its end.

We know that, Electric bulb resistance (R) = 500 ohm (I) = 0.4 A current taken from the source (a) The bulb's power (P) is equal to VI. V = I R V = 0.4500 V (b) At the other end, the potential...

### An electrical appliance has a rating 100 W, 120 V. The resistance of element of appliance when in use is:

(a) 1.2 ohm

(b) 144 ohm

(c) 120 ohm

(d) 100 ohm

When in use, the resistance of the appliance's element is 144 ohm.

### When a current I flows through a resistance R for time t, the electrical energy spent is:

(a) IRt

(b)

(c)

(d) / t

When a current I runs through a resistance R for time t, the electrical energy expended is \({{I}_{2}}RT\)

### Name the factors on which the heat produced in a wire depends when current is passed in it, and state how does it depend on the factors stated by you.

The quantity of heat created in a wire when current is sent through it is determined by the three elements listed below. I The current that flows through the wire (ii) The wire resistance and (iii)...

### Two lamps, one rated 220 V, 50 W and the other rated 220 V, 100 W, are connected in series with mains of voltage 220 V. Explain why does the 50 W lamp consume more power.

A 220 V, 50 W light has a resistance of \({R}_{1}={{V}^{2}}/{{P}_{1}}\) \({R}_{1}={{220}^{2}}/{{100}}\) R1 is equal to 968 ohm. A light with a resistance of 220 V and a power of 100 W is...

### List the names of three electrical gadgets used in your house. Write their power, voltage rating and approximate time for which each one is used in a day. Hence find the electrical energy consumed by each in a month of 30 days.

### An electric bulb is rated ‘100 W, 250 V’. What information does this convey?

When an electric bulb is labelled as "100 W, 250 V," it implies that it consumes 100 W of electricity when powered by a 250 V source (which means 100 J of electrical energy is converted into the...

### What do you mean by power rating of an electrical appliance? How do you use it to calculate (a) the resistance of the appliance and (b) the safe limit of the current in it, while in use?

An electrical item, such as an electric lamp or a geyser, is rated with power (P) and voltage (V) . When an electric bulb is classified as 50 W – 220 V, it implies that it consumes 50 W of...

### Complete the following:

(a) 1 kWh = (1 volt × 1 ampere × ……..) / 1000

(b) 1 kWh= ________ J

(a) \(1KWh=\frac{(1volt\times 1ampere\times 1hour)}{1000}\) (b) \(1KWh=3.6\times {{10}^{6}}\)J

### How do kilowatt and kilowatt-hour differ?

The kilowatt-hour is an electrical energy unit, whereas the kilowatt is an electrical power unit.

### Define the term kilowatt – hour and state its value in S.I. unit.

One kilowatt hour is the amount of electrical energy consumed by a 1 kW electrical appliance when utilised for one hour (kWh). It has a value of 1kWh = \(3.6\times {{10}^{6}}\)J in SI units.

### Name the physical quantity which is measured in (i) kW, (ii) kWh. (iii) Wh

(i) Electrical power is a quantity that is measured in kW. (ii) Electrical energy is the quantity measured in kWh

### (i)State and define the household unit of electricity.

(ii)What is the voltage of the electricity that is generally supplied to a house?

(iii) What is consumed while using different electrical appliances, for which electricity bills are paid?

(i)The residential unit of electricity is the kilowatt hour (kWh). When an electrical device with a power of 1 kW is operated for one hour, the electrical energy used is A kilowatt hour is a unit of...

### State the S.I. unit of electrical power.

The S.I. unit of electrical power is the watt.

### Explain the meaning of the statement ‘the power of an appliance is 100 W’.

An appliance's power is 100 watts. This implies that the device consumes 100 J of electrical energy in a single second.

### Name the S.I. unit of electrical energy. How is it related to Wh?

The S.I. unit of electrical energy is the joule. It has something to do with Wh. 3600 J = 1 Wh

### Electrical power P is given by the expression P = (Q × V) ÷ time

(a)What do the symbols Q and V represent?

(b)Express the power P in terms of current and resistance explaining the meanings of symbols used there in.

(a) The letters Q and V stand for charge and voltage, respectively. \(P={{I}^{2}}R\) (b) Electrical Power -where I stands for current and R stands for resistance

### Write an expression for the electrical power spent in flow of current through a conductor in terms of (a) resistance and potential difference, (b) current and resistance.

(a) In terms of resistance and potential difference, the electrical power expended in current flow through a conductor is expressed as Electrical Power=\(P={{v}_{2}}/R\) (b) In terms of current and...

### Write an expression for the electrical energy spent in flow of current through an electrical appliance in terms of current, resistance and time.

In terms of current, resistance, and time, the electrical energy consumed in the passage of current through an electrical device is expressed as \(W={{I}^{2}}RT\)joule, electrical energy

### A cell of e.m.f. 2 V and internal resistance 1.2 Ω is connected to an ammeter of resistance 0.8 Ω and two resistors of 4.5 Ω and 9 Ω as shown in fig.

Find:

(a) The reading of the ammeter,

(b) The potential difference across the terminals of the cells, and

(c) The potential difference across the 4.5 ohm resistor.

We know that, \({{R}_{eq}}\) = 1.2 + 0.8 + (R1R2) / R1 + R2 \({{R}_{eq}}\) = 2 + 40.5 / 13.5 This implies that \({{R}_{eq}}\) = 5 ohm (a) So, the current is I = \({{E}_{cell}}\) /\({{R}_{eq}}\) I =...

### The diagram below in Fig., shows the arrangement of five different resistances connected to a battery of e.m.f. 1.8 V. Calculate:

a. The total resistance of the circuit

b. The reading of ammeter A.

(a)According to the question, in the diagram given Let us consider that RXY be the resistance between X and Y Therefore, 1 / RXY = 1 / 10 + 1 / 40 1 / RXY = 5 / 40 ohm This implies RXY = 8 ohm Let...

### Three resistors of 6.0 ohm, 2.0 ohm and 4.0 ohm are joined to an ammeter A and a cell of emf 6.0 V as shown in figure. Calculate:

(a) the efective resistance of the circuit.

(b) the reading of ammeter

(a) According to the question, Given R1 = 6 W R’ = R2 + R3 R’ = 2 + 4 R’ = 6 W R1 and R’ are joined in parallel 1 / R = 1 / R1 + 1 / R’ 1 / R = 1 / 6 + 1 / 6 1 / R = 2 / 6 1 / R = 1 / 3 R = 3 ohm...

### The circuit diagram in figure shows three resistors 2 ohm, 4 ohm and R ohm connected to a battery of e.m.f. 2 V and internal resistance 3 ohm. If main current of 0.25 A flows through the circuit, find:

(a) the p.d. across the 4 ohm resistor

(b) the p.d. across the internal resistance of the cell,

(c) the p.d. across the R ohm or 2 ohm resistor, and

(d) the value of R.

(a) According to the question, find p.d. across the resistor of 4 ohm. Given, R = 4 ohm I = 0.25 A Using ohm's law V = IR V = 0.25 × 4 V = 1 V (b) According to the question, find p.d. across the...

### A battery of emf 15 V and internal resistance 3 ohm is connected to two resistors 3 ohm and 6 ohm connected in parallel. Find (a) the current through the battery (b) p.d. between the terminals of the battery (c) the current in 3 ohm resistor (d) the current in 6 ohm resistor.

(a) According to the question, When In parallel 1 / R = 1 / 3 + 1 / 6 1 / R = 1 / 2 R = 2 ohm If r = 3 W ε = 15 V ε = I (R + r) 15 = I (2 + 3) I = 3 A (b) Now find V R = 2 ohm Using ohm's law V =...

### A cell supplies a current of 1.2 A through two 2 ohm resistors connected in parallel. When resistors are connected in series, it supplies a current of 0.4 A. Calculate: (i) the internal resistance and (ii) e.m.f. of the cell.

According to the question, As we know that In parallel R = 1 / 2 + 1 / 2 = 1 ohm I = 1.2 A ε = I (R + r) ε = 1.2 (1 + r) ε = 1.2 + 1.2r In series R = 2 + 2 R = 4 ohm I = 0.4 A ε = I (R + r) ε = 0.4...

### A particular resistance wire has a resistance of 3 ohm per meter. Find:

(a) The total resistance of three lengths of this wire each 1.5 m long, in parallel.

(b) The potential difference of the battery which gives a current of 2 A in each of the 1.5 m length when connected in the parallel to the battery (assume that resistance of the battery is negligible).

(c) The resistance of 5 m length of a wire of the same material, but with twice the area of cross section

(a) Wire resistance per metre = 3 ohm As a result, the resistance of three 1.5 m long sections of this wire = 3 × 1.5 = 4.5 W 1 / R = 1 / 4.5 + 1 / 4.5 + 1 / 4.5 1 / R = 3 / 4.5 R = 1.5 ohm (b) I =...

### In figure, calculate :

(a) the total resistance of the circuit.

(b) the value of R, and

(c) the current flowing in R

(a) According to the question,, find the total resistance of the circuit. V = 4 V I = 0.4 A Total resistance R’ =? R’ = V / I R’ = 0.4 / 4 R’ = 10 ohm (b) To calculate the value of R R1 = 20 ohm R’...

### Calculate the current flowing through each of the resistors A and B in the circuit shown in figure?

According to the question, For resistor A R = 1 ohm V = 2 V I = V / R I = 2 / 1 I = 2 A For resistor B R = 2 ohm V = 2 V I = V / R I = 2 / 2 I = 1 A Thus, current passing in resistor A is 2 A and...

### Two resistors of resistance 4 Ω and 6 Ω are connected in parallel to a cell to draw 0.5 A current from the cell.

(a) Draw a labeled diagram of the arrangement

(b) Calculate current in each resistor.

(a) Circuit diagram (b) Equivalent resistance of the circuit 1 / R = 1 / 4 + 1 / 6 1 / R = (3 + 2) / 12 1 / R = 5 / 12 R = 12 / 5 R = 2.4 ohm Hence, the e.m.f. of the cell is V = IR V = 0.5 × 2.4 V...

### A resistor of 6 ohm is connected in series with another resistor of 4 ohm. A potential difference of 20 V is applied across the combination. (a) Calculate the current in the circuit and (b) potential difference across the 6 ohm resistor.

(a) According to the question, calculate current in the circuit R1 = 6 ohm R2 = 4 ohm R = R1 + R2 R = 6 + 4 R = 10 ohm V = 20 V I = V / R I = 20 / 10 I = 2 A (b) To find the voltage across the...

### Two resistors of 2 ohm and 3 ohm are connected (a) in series, (b) in parallel, with a battery of 6.0 V and negligible internal resistance. For each case draw a circuit diagram and calculate the current through the battery.

According to the question, (a)R1 = 2 ohm R2 = 3 ohm R = R1 + R2 R = 2 + 3 R = 5 ohm V = 6 V Now, I = V / R I = 6 / 5 I = 1.2 ohm when, R1 and R2 are joined in parallel 1 / R = 1 / R1 + 1 / R2...

### Five resistors, each of 3 ohm, are connected as shown in figure. Calculate the resistance (a) between the points P and Q, and (b) between the points X and Y.

According to the question, (a) R1 = 3 + 3 R1 = 6 ohm R2 = 3 ohm R1 and R2 are joined in parallel 1 / R = 1 / R1 + 1 / R2 1 / R = 1 / 6 + 1 / 3 1 / R = (1 + 2) / 6 1 / R = 3 / 6 1 / R = 1 / 2 R = 2...

### In the network shown in adjacent figure, calculate the equivalent resistance between the points (a) A and B (b) A and C

According to the question, (a) R1 = 2 + 2 + 2 R1 = 6 ohm R2 = 2 ohm R1 and R2 are joined in parallel 1 / R = 1 / R1 + 1 / R2 1 / R = 1 / 6 + 1 / 2 1 / R = (1 + 3) / 6 1 / R = 4 / 6 R = 6 / 4 R = 1.5...

### Calculate the equivalent resistance between the points A and B in figure

According to the question, R1 = 3 + 2 = 5 ohm R2 = 30 W R3 = 6 + 4 = 10 ohm If the resistors R1, R2 and R3 are connected in parallel 1 / R = 1 / R1 + 1 / R2 + 1 / R3 1 / R = 1 / 5 + 1 / 30 + 1 / 10...

### Calculate the effective resistance between the points A and B in the network shown below in figure.

According to the question, If the R is parallel 1 / R = 1 / 12 + 1 / 6 + 1 / 4 1 / R = (1 + 2 + 3) / 12 1 / R = 6 / 12 R = 12 / 6 R = 2 ohm Now, if the resistances are in series R = 2 + 2 + 5 R = 9...

### A circuit consists of a 1 ohm resistor in series with a parallel arrangement of 6 ohm and 3 ohm resistors. Calculate the total resistance of the circuit. Draw a diagram of the arrangement.

According to the question,. 1 / r = 1 / 6 + 1 / 3 1 / r = 1 / 2 r = 2 ohm R = 2 + 1 R = 3 ohm

### A uniform wire with a resistance of 27 ohm is divided into three equal pieces and then they are joined in parallel. Find the equivalent resistance of the parallel combination.

The new resistance = 27 / 3 = 9 due to the wire being divided into three pieces. Three resistances are now linked in a parallel fashion. 1 / r = 1 / r1 + 1 / r2 + 1 / r3 1 / r = 1 / 9 + 1 / 9 + 1 /...

### Calculate the effective resistance between the points A and B in the circuit shown in figure

In the diagram above, Between XAY = (1 + 1 + 1), there is a resistance. = 3 ohm Between XY = 2 ohm, there is a resistance of 2 ohm. Between XBY = 6 ohm, there is a resistance of 6 ohm. Allow R' to...

### In the circuit shown below in figure, calculate the value of x if the equivalent resistance between the points A and B is 4 ohm

According to the question, r1 = 4 ohm r2 = 8 ohm r3 = x ohm r4 = 5 ohm r = 4 ohm r’ = r1 + r2 r’ = 4 + 8 Hence, r’ = 12 ohm r’’ = r3 + r4 r’’ = (x + 5) ohm 1 / r = 1 / r’ + 1 / r’’ 1 / 4 = 1 / 12 +...

### A combination consists of three resistors in series. Four similar sets are connected in parallel. If the resistance of each resistor is 2 ohm, find the resistance of the combination.

Resistance of every set: r1 = 2 + 2 + 2 = 6 ohm r2 = 2 + 2 + 2 = 6 ohm r3 = 2 + 2 + 2 = 6 ohm r4 = 2 + 2 + 2 = 6 ohm Now, when the these resistances are put in parallel 1 / r = 1 / r1 + 1 / r2 + 1 /...

### Calculate the equivalent resistance between the points A and B in figure if each resistance is 2.0 Ω

For a parallel resistances Reff = (R1R2) / (R1 + R2) Reff = (2 × 2) / (2 + 2) Reff = 4 / 4 Reff = 1 Ω Therefore, total resistance = 2 + 2 + 1 = 5 Ω

### Three resistors each of 2 W are connected together so that their total resistance is 3 W. Draw a diagram to show this arrangement and check it by calculation.

In series with one resistor, a parallel combination of two resistors. R1 = 2 ohm R2 = 2 ohm R3 = 2 ohm 1 / R’ = 1 / R1 + 1 / R2 1 / R’ = 1 / 2 + 1 / 2 1 / R’ = 1 R’ = 1 ohm R = R’ + R3 R = 1 + 2 R =...

### You have three resistors of values 2 Ω, 3 Ω and 5 Ω . How will you join them so that the total resistance is less than 1 Ω? Draw diagram and find the total resistance.

The three resistors should be linked in parallel to get a total resistance of less than one. Let the total resistance be R’ Then, 1 / R’ = 1 / 2 + 1 / 3 + 1 / 5 1 / R’ = (15 + 10 + 6) / 30 1 / R’ =...

### Four resistors each of resistance 2 ohm are connected in parallel. What is the effective resistance?

According to the question, R1 = 2 ohm R2 = 2 ohm R3 = 2 ohm R4 = 2 ohm 1 / R = 1 / R1 + 1 / R2 + 1 / R3 + 1 / R4 1 / R = 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2 1 / R = 2 Hence, R = 0.5...

### Two resistors having resistance 4 ohm and 6 ohm are connected in parallel. Find their equivalent resistance.

Let R' be the equivalent resistance of the paralleled 4 ohm and 6 ohm resistors. Then, 1 / R’ = 1 / 4 + 1 / 6 = (3 + 2) / 12 = 5 / 12 ohm or R’ = 12 / 5 R’ = 2.4 ohm

### A cell of e.m.f. ε and internal resistance r sends current 1.0 A when it is connected to an external resistance 1.9 ohm. But its sends current 0.5 A when it is connected to an external resistance of 3.9 ohm. Calculate the values of e and r.

In the first instance, I = 1 A, R = 1.9 ohm ε = I (R + r) = 1 (1.9 + r) = 1.9 + r [1] In the second scenario, I = 0.5 A, R = 3.9 ohm ε = I (R + r) = 0.5 (3.9 + r) = 1.95 + 0.5r [2] [1] and [2] are...

### A battery of emf 15 V and internal resistance 3 ohm is connected to two resistors of resistances 3 ohm and 6 ohm in series. Find:

(a) the current through the battery

(b) the p.d. between the terminals of the battery.

According to the question, (a) ε = 15 V R = 6 + 3 R = 9 ohm r = 3 ohm I =? I = ε / (R + r) I = 15 / (9 + 3) I = 15 / 12 I = 1.25 A (b) Current I = 1.25 A [calculated in part (a)] External resistance...

### A cell of emf 1.8 V and internal resistance 2 ohm is connected in series with an ammeter of resistance 0.7 ohm and resistance of 4.5 ohm as shown in figure.

(a) What would be the reading of the ammeter?

(b) What is the potential difference across the terminals of the cell?

According to the question, (a) ε = 1.8 V Total resistance = 2 + 4.5 + 0.7 = 7.2 W I =? I = ε / R I = 1.8 / 7.2 I = 0.25 A (b) I = 0.25 A [calculated in (a) part] internal resistance total resistance...

### A battery of e.m.f. 3.0 V supplies current through a circuit in which resistance can be changed. A high resistance voltmeter is connected across the battery. When the current is 1.5 A, the voltmeter reads 2.7 V. Find the internal resistance of the battery.

According to the question, ε = 3 volt I = 1.5 A V = 2.7 V V = ε – Ir r = (e – V) / I r = (3 – 2.7) / 1.5 Therefore, r = 0.2 ohm

### The diagram in figure shows a cell of e.m.f. ε = 2 volt and internal resistance r = 1 ohm connected to an external resistance R = 4 ohm. The ammeter A measures the current in the circuit and the voltmeter V measures the terminal voltage across the cell. What will be the readings of the ammeter and voltmeter when (i) the key K is open, and (ii) the key K is closed

(i) Ammeter reading = 0 , due to lack of current Voltage V = ε – Ir V = 2 – 0 × 1 V = 2 volt (ii) The reading on the ammeter I = ε / (R + r) I = 4 + 1 / 2 I = 2/5 I=0.4 amp Measurement of voltage...

### Which of the following combinations have the same equivalent resistance between X and Y?

In figure (a), the resistors are connected in parallel between X and Y. Let R' be the resistance they have in common. 1 / R' now equals 1 / 2 + 1 / 2 = 2 / 2 ohm ohm ohm ohm ohm o [1] R' = 1 ohm In...

### In parallel combination of resistances:

(a) P.D. is same across each resistance

(b) Total resistance is increased

(c) Current is same in each resistance

(d) All of the above are true

In a parallel combination of resistances, P.D is the same for each resistance.

### In series combination of resistances:

(a) P.d. is same across each resistance

(b) Total resistance is reduced

(c) Current is same in each resistance

(d) All of the above are true

Each resistance in a sequence of resistances has the same current.

### The V-I graph for a series combination and for a parallel combination of two resistors is shown in fig. Which of the two, A or B, represents the parallel combination? Give a reason for your answer.

The straight line A has a smaller change in V than the straight line B. (which means the straight line A is less steeper than B). As a result, the straight line A denotes low resistance, whereas the...

### State how are the two resistors joined with a battery in each of the following cases when:

(a) same current flows in each resistor

(b) potential difference is same across each resistor.

(c) equivalent resistance is less than either of the two resistances.

(d) equivalent resistance is more than either of the two resistances.

(a) The two resistors are connected in parallel. (b) The two resistors are connected in series. (c) The two resistors are connected in series. (d) The two resistors are connected in parallel.

### Show by a diagram how two resistors R1 and R2 are joined in parallel. Obtain an expression for the total resistance of the combination.

Using Ohm’s law separately to the two resistors, I1 = V / R1 I2 = V / R2 I = I1 + I2 V / R = V / R1 + V / R2 1 / R = 1 / R1 + 1 / R2

### How would you connect two resistors in series? Draw a diagram. Calculate the total equivalent resistance.

If current I is taken from the battery, the current through each resistor will also be I. When we individually apply Ohm's law to the two resistors, we get: V1 = IR1 V2 = IR2 V = V1 + V2 IR = IR1 +...

### Write the expressions for the equivalent resistance R of three resistors R1, R2 and R3 joined in (a) parallel, (b)

(a) Total parallel resistance is equal to 1 / R = 1 / R1 + 1 / R2 + 1 / R3 (b) Total series resistance is equal to R1 + R2 + R3 = R3

### Explain why the p.d. across the terminals of a cell is more in an open circuit and reduced in a closed circuit.

When the electric cell is in a closed circuit, current flows across the circuit. There is a possible drop across the cell's internal resistance. As a result, the potential drop across the terminals...

### A cell is used to send current to an external circuit. (a) How does the voltage across its terminal compare with its emf? (b) Under what condition is the emf of the cell equal to its terminal voltage?

(a) A cell's terminal voltage V is smaller than its e.m.f. when current is taken from it. ∴ Terminal voltage < e.m.f. (b) The e.m.f. is equal to the terminal voltage when no current is...

### A cell of e.m.f. ε and internal resistance r is used to send current to an external resistance R. Write expressions for (a) the total resistance of circuit, (b) the current drawn from the cell, (c) the p.d. across the cell, and (d) voltage drop inside the cell.

(a) total resistance = R + r (b) The amount of current drained from the cell ε = V + v = IR + Ir = I (R + r) I = ε / (R + r) (c) p.d. across the cell: [ε / (R + r)] × R (d) voltage drop inside the...

### Name two factors on which the internal resistance of a cell depends and state how does it depend on the factors stated by you.

The following are the variables that influence a cell's internal resistance: I The electrode surface area - the greater the electrode surface area, the lower the internal resistance. (ii) The...

### State two differences between the e.m.f. and terminal voltage of a cell.

E.M.F Cell 1.It is a property of the cell, meaning it is independent of the amount of current pulled from cell 2. When the cell is not in use, it is equal to the terminal voltage, but when the cell...

### Explain the meaning of the terms e.m.f., terminal voltage and internal resistance of cell.

e.m.f. : The electromotive force, or e.m.f., is the potential difference between the terminals of a cell while it is in open circuit. The potential difference between the electrodes of the cell is...

### The filament of a bulb takes a current 100 mA when potential difference across it is 0.2 V. When the potential difference across it becomes 1.0 V, the current becomes 400 mA. Calculate the resistance of filament in each case and account for the difference.

Using Ohm’s law V = IR R = V / I R1 = V1 / I1 R1 = 0.2 / 0.1 R1 = 2 ohm Simultaneously R2 = V2 / I2 R2 = 1 / 0.4 R2 = 2.5 ohm The wire's resistance increases as the temperature rises. As a result,...

### What length of copper wire of specific resistance ohm m and radius 1 mm is required so that its resistance is 1 ohm.

According to the question, R = 1 ohm Specific resistance = 1.7× 10-8 ohm m r = 10-3 m l =? R = ρ 1 / A l = RA / ρ l = Rπr2 / ρ l = (1 × π × 10-6) / (1.7 × 10-8) l = (1 × 3.14 × 10-6) / (1.7 × 10-8)...

### A wire of resistance 9 Ohm having length 30 cm is tripled on itself. What is its new resistance?

According to the question, R = 9 Ohm l = 30 cm Let New length be l’ = 3 × l and new resistance R’=? With a change in length, the area of the cross section will vary in the same order. R’ = ρ (l / 3...

### A wire of resistance 3 Ohm and length 10 cm is stretched to length 30 cm. Assuming that it has a uniform cross-section, what will be its new resistance?

According to the question, R = 3 Ohm l = 10 cm we get the new length as l’ = 30 cm = 3 × l R = ρ (l / A) As a result, new resistance In the same sequence, stretching length will grow and cross...

### A given wire of resistance 1 Ohm is stretched to double its length. What will be its new resistance?

Let ‘I' be the length of the resistor and ‘a' be the cross-sectional area of the resistor with resistance R = 1 Ohm. When a wire is stretched to double its original length, As a result, length l' =...

### Two wires of the same material and same length have radii 1 mm and 2 mm respectively. Compare (i) their resistances (ii) their specific resistance.

(i) When the radius of wire is r1 R1 = ρ (l / A1) R1 = ρ (l / πr12) (ii) When the radius of wire is r2 R2 = ρ (l / A2) R2 = ρ (l / πr22) ∴ R1: R2 will be ρ (l / πr12) : ρ (l / πr22) = r22: r12 (ii)...

### In an experiment of verification of Ohm’s law, following observations are obtained.

Draw a characteristic V-I graph and use this graph to find:

(a) potential difference V when the current I is 0.5 A.

(b) current I when the potential difference V is 0.75 V.

(c) resistance in circuit

(a) When the current is 0.5 A, the potential difference is 1.25 V. (b) When the potential difference is 0.75 V, current is 0.3 A. (c) Because the graph is linear, resistance may be calculated from...

### Calculate the current flowing through a wire of resistance 5 Ohm connected to a battery of potential difference 3 V.

According to the question, V = 3 V R = 5 Ohm I =? On using Ohm’s law I = V / R I = 3 / 5 Therefore, I = 0.6 A

### A car bulb connected to a 12 volt battery draws 2 A current when glowing. What is the resistance of the filament of the bulb? Will the resistance be more, same or less when the bulb is not glowing.

According to the question, V = 12 V I = 2 A R =? Using Ohm’s law R = V / I R = 12 / 2 R = 6 Ohm Therefore, if bulb is not lighting, resistance will be low

### An electric bulb draws 1.2 A current at 6.0 V. Find the resistance of filament of bulb while glowing.

According to the question, I = 1.2 A V = 6.0 V R =? On using Ohm’s law R = V / I R = 6 / 1.2 R = 5 Ohm

### Find the potential difference required to flow a current of 200 mA in a wire of resistance 20 ohm.

According to the question, I = 0.2 A R = 20 ohm V =? We know that, V = IR V = 0.2 × 20 V = 4 V

### A current of 1.6 mA flows through a conductor. If charge of an electron is coulomb, find the number of electrons that will pass each second through the cross section of that conductor

According to the question, I = 1.6 × 10-3 A Q = -1.6 × 10-19 coulomb t = 1 s We know I = Q / t From here, Q = 1.6 × 10-3 × 1 Therefore, Number of electrons = 1.6 × 10-3 / 1.6 × 10-19 =...

### In a conductor, electrons flow from its end A to B in 2 s. Find the current flowing through the conductor.

Given The number of electrons that pass across a conductor, The number of electrons in n =\(6.25\times {{10}^{16}}\) is the number of electrons in n = \(6.25\times {{10}^{16}}\) The time it takes to...

### For which of the following substances, resistance decreases with increase in temperature?

(a) Copper

(b) Mercury

(c) Carbon

(d) Platinum

For carbon, resistance diminishes as temperature rises.

### Which of the following is an ohmic resistance?

(a) LED

(b) Junction diode

(c) Filament of a bulb

(d) Nichrome wire

Nichrome wire is an ohmic resistance.

### Name the material used for making a fuse wire. Give a reason.

Because of its high resistivity and low melting point, a lead-tin alloy is utilised to make fuse wire.

### (a) Name the material used for making the connection wires. Give reason for your answer. (b) Why should a connection wire be thick?

(a) Copper or aluminium are the materials utilised to make connection wires because they have a low specific resistance and hence have low resistance in their wires. (b) The connecting wires are...

### How does (a) resistance, and (b) specific resistance of a wire depend on its (i) length, and (ii) radius?

(a) Resistance is proportional to the wire's length and inversely proportional to the square of the wire's radius. (b) A wire's specific resistance is not affected by the length or radius of the...

### How does specific resistance of a semi-conductor change with the increase in temperature?

The particular resistance of a semi-conductor reduces as the temperature rises.

### Name a substance of which the specific resistance remains almost unchanged by the increase in temperature.

Manganin is a chemical whose specific resistance remains nearly constant when the temperature rises.

### (a) Name two factors on which the specific resistance of a wire depends? (b) Two wires A and B are made of copper. The wire A is long and thin while the wire B is Short and thick. Which will have more specific resistance?

(a) A wire's particular resistance is determined by two elements. I The substance's material and (ii) The substance's temperature (a) Because the specific resistance of a wire is determined by its...

### State the order of specific resistance of (i) a metal, (ii) a semiconductor and (iii) an insulator.

I Metals have a low specific resistance because they enable the majority of current to flow through them. (ii) Semiconductors have a higher specific resistance than metals. (iii) Insulators have a...

### Write an expression connecting the resistance of a wire and specific resistance of its material. State the meaning of symbols used.

The term used is R = ρ l / a where ρ = the conductor's material's specific resistance R = conductor resistance l = conductor length A = conductor cross-sectional area

### Define the term specific resistance and state its S.I. unit.

A material's specific resistance is the resistance of a wire of that material of unit length and cross section area. The ohm metre is the SI unit of specific resistance.

### Name three factors on which the resistance of a wire depends and state how it is affected by the factors stated by you?

The following are the three variables that influence wire resistance: (i)A wire's resistance is proportionate to its length, that is, R ∝ l (ii) A wire's resistance varies inversely with its cross...

### Two wires, one of copper and other of iron, are of the same length and same radius. Which will have more resistance? Give reason.

Iron has a higher resistivity than copper, which has a lower resistance. As a result, the higher the resistivity, the larger the resistance; conversely, the lower the resistivity, the lower the...

### How does the resistance of a metallic wire depend on its temperature? Explain with reason.

The random motion of electrons increases as the temperature of a conductor rises. As a result, the number of collisions between electrons and positive ions increases. When a result, as the...

### How does the resistance of a wire depend on its length? Give a reason of your answer.

The length of a wire is directly proportional to its resistance. R ∝ l The resistance of a conductor is determined by the number of collisions that an electron has with fixed positive ions as it...

### (a) How does the resistance of a wire depend on its radius? Explain your answer.

(b) Two copper wires are of same length, but one is thicker than the other. Which will have more resistance?

The resistance of a wire changes inversely with its cross-sectional area, i.e., R ∝ 1 / a R ∝ 1 / π2 The resistance of a wire is proportional to its length, i.e., R l, and inversely proportional to...

### Draw a V – I graph for a conductor at two different temperatures. What conclusion do you draw from your graph for the variation of resistance of conductor with temperature?

T1 > T2 in the graph shown above. Because conductor resistance is higher at high temperature T1 than at low temperature T2, the straight line A is steeper than the line B. As a result, we may...

### Fig. below shows the I-V characteristic curves for two resistors. Identify the ohmic and non-ohmic resistors. Give a reason for your answer.

The resistors in graphs (a) and (b) are non-ohmic and ohmic, respectively. The I-V graph for (a) is a curve, but the I-V graph for (b) is a straight line or linear.

### Give two differences between an ohmic and non-ohmic resistor

Ohmic resistor It follows Ohm's law, which states that V / I is constant for all V or I values. At a given temperature, the slope of the V-I graph is the same for all values of V or I. Non-ohmic...

### What are non-ohmic resistors? Give one example and draw a graph to show its current-voltage relationship.

Non-ohmic resistors (also known as non-linear resistances) are conductors that do not obey Ohm's law. LEDs, solar cells, junction diodes, and other similar devices are examples.

### What is an ohmic resistor? Give one example of an ohmic resistor. Draw a graph to show its current – voltage relationship. How is the resistance of the resistor determined from this graph?

Ohmic resistors, often known as linear resistances, are conductors that follow Ohm's law. Silver, aluminium, copper, iron, and other metallic conductors are examples.

### Draw a I-V graph for a linear resistor. What does its slope represent?

A linear resistor's I-V graph Slope of the I-V graph: I / V is the slope of the I-V graph. ΔI / ΔV is the reciprocal resistance of the conductor i.e. Slope = ΔI / ΔV = 1 / resistance of the...

### (a) Draw a V-I graph for a conductor obeying Ohm’s law.

(b) What does the slope of V-I graph for a conductor represent?

(a) The V-I graph for a conductor obeying Ohm's law is shown below. (b) The slope of a conductor's V-I graph reflects resistance.

### (a) Name and state the law which relates the potential difference and current in a conductor.

(b) What is the necessary condition for a conductor to obey the law named above in part (a)?

(a)Ohm's law is the name of the law. The current flowing through a conductor is exactly proportional to the potential difference at its ends, assuming that the conductor's physical parameters and...

### State Ohm’s law and draw a neat labelled circuit diagram containing a battery, a key, a voltmeter, an ammeter, a rheostat and an unknown resistance to verify it.

The current flowing through a conductor is exactly proportional to the potential difference applied across its ends, according to Ohm's law, assuming that the physical parameters and temperature of...

### (a) Name the particles which are responsible for the flow of current in a metallic wire.

(b) Explain the flow of current in a metallic wire on the basis of movement of the particles named by you above in part (a).

(c) What is the cause of resistance offered by the metallic wire in the flow of current through it?

(a) In a metallic wire, free electrons are the particles responsible for current flow. (b) In metals, free electrons are the moving charges that cause electricity to conduct. If ‘n' electrons pass...

### Define the term resistance. State its S.I. unit.

The obstruction offered to the flow of current by the conductor is known as its resistance. The S.I. unit of resistance is Ohm.

### (a) State whether the current is a scalar or vector? What does the direction of current convey?

(b) State whether the potential is a scalar or vector? What does the positive and negative sign of potential convey?

(a) Current is a scalar quantity. The direction of current conveys that the electrons flow opposite to the direction of flow of current. (b) Potential is a scalar quantity. The positive sign of...

### Explain the statement ‘the potential difference between two points is 1 volt’.

The potential difference between two points is said to be 1 volt when 1 joule of work is done in bringing 1 coulomb charge from infinity to that point

### How is the electric potential difference between the two points defined? State its S.I. unit.

The potential difference between two points can be defined as the potential difference between two points is equal to the work done per unit charge in moving a positive test charge from one point to...

### Define the term electric potential. State it’s S.I. unit.

The amount of work done per unit charge in bringing a positive test charge from infinity to that point is known as electric potential at a point. The S.I. unit of electric potential is volt.

### Define the term current and state its S.I. unit.

The rate of flow of charge is known as current. The S.I. unit of current is Ampere.

**A total reflecting equilateral prism can be used to deviate a ray of light through:**

a. 30° b. 60° c. 75° d. 90° Solution: A complete reflecting equilateral prism can be used to bend a light ray by 60 degrees.

**A total reflecting right-angled isosceles prism can be used to deviate a ray of light through**

a. 30° b. 60° c. 75° d. 90° Solution: To deviate a ray of light through 90 degrees, use a complete reflecting right angled isosceles prism.

**The critical angle for the glass-air interface is :**

a. 24° b. 48° c. 42° d. 45° Solution: The correct option is (c) - 42 degrees

**State one advantage of using a total reflecting prism as a reflector in place of a plane mirror.**

Solution: The picture produced by a total reflecting prism is much brighter and the brightness remains constant even after extended use. But the image produced by a plane mirror is less brilliant...

**Mention one difference between the reflection of light from a plane mirror and total internal reflection of light from a prism.**

Solution: In total internal reflection of light from a prism, all of the incident light is reflected back into the denser medium. Whereas in conventional reflection from a plane mirror, only a...

### Two isosceles right-angled glass prisms P and Q are placed near each other as shown in Fig. Complete the path of the light ray entering the first prism till it emerges out of the second prism Q.

Solution :

**Draw a neat labelled ray diagram to show the total internal reflection of a ray of light normally incident on one face of a 30°, 90°, 60° prism.**

Solution:

**In Fig., a ray of light PQ is incident normally on the face AB of an equilateral glass prism. Complete the ray diagram showing its emergence into air after passing through the prism.**

Take critical angle for glass = 42° (a)Write the angles of incidence at the faces AB and AC of the prism. (b)Name the phenomenon which the ray of light suffers at the face AB, AC and BC of the...

### In Fig., a ray of light PQ is incident normally on the hypotenuse of an isosceles right angle prism ABC.

(a) Complete the path of the ray PQ until it emerges from the prism. Mark in the diagram the angle wherever necessary. (b) What is the angle of deviation of the ray PQ? (c) Name a device in which...

**A ray of light OP passes through a right-angled prism as shown in the adjacent diagram.**

(a)State the angles of incidence at the faces AC and BC. (b)Name the phenomenon which the ray suffers at the face AC. Solution: (a) The incidence angle at the face AC is 45 degrees, while the...

**Show with the help of a diagram how a total reflecting prism can be used to turn a ray of light through 90°. Name one instrument in which such a prism is used.**

Solution: A beam of light is incident normally at the face AB in the illustration above. As a result, it passes through the prism undeviated and strikes the face AC at a 45-degree angle of...

**What is a total reflecting prism? State three actions that it can produce. Draw a diagram to show one action of the total reflecting prism.**

Solution: A fully reflecting prism is described as a prism with an angle of 900 between its two refracting surfaces and two additional angles of 450 each. When light is incident ordinarily on any of...

### A ray of light enters a glass ABCD as shown in Fig. and strikes at the Centre O of the circular part AC of the slab. The critical angle of glass is 42°. Complete the path of the ray till it emerges out from the slab. Mark the angles in the diagram wherever necessary.

Solution : At its crucial angle, the beam strikes the glass. As a result, the refraction angle will be 90 degrees.

**The refractive index of glass is 1.5. From a point P inside a glass block, draw rays PA, PB and PC incident on that glass-air surface at an angle of 30**^{o}, 42^{o} and 60^{o} respectively.

^{o}, 42

^{o}and 60

^{o}respectively.

(a)In the diagram show the approximate direction of these rays as they emerge out of the block. (b)What is the angle of refraction for the ray PB? Solution: (a) According to the question, refractive...

### In the figure, PQ and PR are the two light rays emerging from an object P. The ray PQ is refracted as QS.

(a) State the special name given to the angle of incidence ∠PQN of the ray PQ. (b) What is the angle of refraction for the refracted ray QS? (c)Name the phenomenon that occurs if the angle of...

**Fig. shows a point source P inside a water container. Three rays A, B and C starting from the source P are shown up to the water surface.**

(a) Show in the diagram, the path of these rays after striking the water surface. The critical angle for water-air surface is 48°. (b) Name the phenomenon which the rays A, B and C exhibit. Solution...

### Figure below show two rays A and B travelling from water to air. If the critical angle for water- air surface is 48°, complete the ray diagram showing the refracted rays for each. State conditions when the ray will suffer total internal reflection.

Solution ; There are two prerequisites for total introspective reflection: (i) Light must pass through a denser media before reaching a rarer medium. (ii) The incidence angle must be larger than or...

**The refractive index of air with respect to glass is expressed as **_{g}μ_{a} = sin i / sin r

_{g}

(a) Write down a similar expression for aμg in terms of angle i and r. (b) If angle r = 900, what is the corresponding angle i called? (c) What is the physical significance of the angle i and part...

**State whether the following statement is true or false:**

If the angle of incidence is greater than the critical angle, light is not refracted at all, when it falls on the surface from a denser medium to a rarer medium. Solution: This statement is true....

### Fill in the blanks to complete the following sentences:

(a) When a ray of light moves from a denser media to a rarer medium, _____________ happens. (b) The ____________ is the angle of incidence in a denser medium for which the refraction angle in a...

**(a)What is total internal reflection?**

(b)State two conditions necessary for total internal reflection to occur. (c)Draw diagrams to illustrate critical angle and total internal reflection. Solution: (a) Total internal reflection: A beam...

**The critical angle for glass-air is 45° for the light of yellow colour. State whether it will be less than, equal to, or more than 45° for (i) red light, (ii) blue light?**

Solution: The refractive index increases (or drops) when the wavelength of light decreases (or increases), and the critical angle decreases (or more) (i) The crucial angle for red light will be more...

**Name two factors which affect the critical angle for a given pair of media. State how do the factors affect it.**

Solution: The crucial angle is influenced by two factors. (a) The wavelength or colour of light, and (b) The ambient temperature Effect on light colour: For a pair of media, the critical angle is...

**A light ray is incident from a denser medium on the boundary separating it from a rarer medium at an angle of incidence equal to the critical angle. What is the angle of refraction for the ray?**

Solution: When a beam is incident from a denser media to a rarer medium at an angle of incidence equal to the critical angle, the angle of refraction becomes 90 degrees.

**What is the meant by the statement ‘the critical angle for diamond is 24°?**

Solution: The phrase "the critical angle for diamond is 24° suggests that at a 24° incidence angle, the angle of refraction in the air will reach 90° within the diamond. When the incidence angle...

**State the approximate value of the critical angle for**

(a) glass-air surface (b) water-air surface. Solution: (a) According to the question, refractive index aμg = 3 / 2 Therefore, critical angle for glass – air surface is given by - sin...

**How is the critical angle related to the refractive index of a medium?**

Solution: The relationship between critical angle and a medium's refractive index is known as the critical angle-refractive-index relationship. μ = 1 / sin C = cosec C

**Explain the term critical angle with the aid of a labelled diagram.**

Solution: The critical angle is the angle of incidence in the denser medium that corresponds to the angle of refraction in the rarer media of 90 degrees.

**A postage stamp kept below a rectangular glass block or refractive index 1.5 when viewed from vertically above it, appears to be raised by 7.0 mm. Calculate the thickness of the glass block.**

Solution: According to the question, refractive index of the glass block (μg) is 1.5 and the shift in the image is 7 mm or 0.7 cm We have to determine the thickness of glass block or real depth...

**A coin is placed at the bottom of a beaker containing water (refractive index = 4/3) to a depth of 12 cm. By what height the coin appears to be raised when seen from vertically above?**

Solution: According to the question, refractive index of the water (μw) is 4 / 3 and the real depth of coin is 12 cm We have to find the shift in the image Expression for the shift in image in terms...

**A water pond appears to be 2.7 m deep. If the refractive index of water is 4/3, find the actual depth of the pond.**

Solution: According to the question, apparent depth is 2.7 m and the refractive index of water (μw) is 4 / 3 Therefore, using the expression of refractive index we can write => Real depth = Apparent...

**An object in a denser medium when viewed from a rarer medium appears to be raised. The shift is maximum for:**

a. Red light b. Violet light c. Yellow light d. Greenlight Solution: The correct option is (b) - violet light. The shift is greatest for violet light because violet light has the...

**A small air bubble in a glass block when seen from above appears to be raised because of:**

a. Refraction of light b. Reflection of light c. Reflection and refraction of light d. None of the above Solution: The correct option is (a). A spherical air bubble in glass...

**An object placed in one medium when seen from the other medium, appears to be vertically shifted. Name the factors on which the magnitude of shift depends and state how does it depend on them.**

Solution: The apparent elevation of the item is determined by: (i) The medium's refractive index. (ii) The denser medium's thickness and (iii) The wavelength or colour of incoming light The shift...

**A student puts his pencil into an empty trough and observes the pencil from the position as indicated in the Fig.**

(i) What change will be observed in the appearance of the pencil when water is poured into the trough? (ii) Name the phenomenon which accounts for the above-started observation....

**A fish is looking at a 1.0 m high plant at the edge of the pond. Will the plant appear shorter or taller than its actual height? Draw a ray diagram to support your answer.**

Solution: The plant will appear to be taller than its real height. Allow the fish to gaze from point O. Because air is a rarer material than water, when the ray OP comes from the water into air, it...

**Draw a ray diagram to show the appearance of a stick partially immersed in water. Explain your answer.**

Solution: A stick appears bent or lifted in the above image, which is partially immersed in water in a glass container. This is because the rays appear to be coming from P', which is a virtual image...

**Water in a pond appears to be only three-quarters of its actual depth. (a) What property of light is responsible for this observation? Illustrate your answer with the help of a ray diagram. (b) How is the refractive index of water calculated from its real and apparent depths?**

Solutions: (a) This observation is due to refraction of light. Light is bent away from the normal due to refraction from a denser media to a rarer medium. (b) Assume that an object B is located at...

**A tank of water is viewed normally from above.**

(a) State how the depth of tank appears to change. (b) Draw a labelled ray diagram to explain your answer. Solution: (a) The depth of the tank seems to be less than its true depth due to light...

**Prove that**

Refractive index = Real depth / Apparent depth Solution: Take a look at a ray of light. OA is generally incident on the surface PQ. It follows AA' in a straight line. Consider another beam from O...

**How is the refractive index of a medium related to the real and apparent depths of an object in that medium?**

Solution: The refractive index μ is related to the real and apparent depths in the following manner - μ = Real Depth / Apparent Depth

**What should be the angle of incidence for a ray of light which suffers a minimum deviation of 36**^{o} through an equilateral prism?

^{o}through an equilateral prism?

Solution: According to the question, the angle of prism is A = 600 And the angle of minimum deviation is ????min = 360 We have to find the angle of incidence, i Expression of minimum deviation is...

**A ray of light incident at an angle 48**^{o} on a prism of refracting angle 60^{o} suffers minimum deviation. Calculate the angle of minimum deviation.

^{o}on a prism of refracting angle 60

^{o}suffers minimum deviation. Calculate the angle of minimum deviation.

Solution: According to the question, the angle of incidence is i = 480 And the angle of refraction is A = 600 We have to determine the angle of minimum deviation, ????min Expression of the angle of...

**A ray of light suffers refraction through an equilateral prism. The deviation produced by the prism does not depend on the:**

(a) angle of incidence (b) colour of light (c) material of prism (d) size of prism Solution: The correct option is (d). The deviation of a prism is determined by:Prism refractive index- The...

**In refraction of light through a prism, the light ray:**

a. Suffers refraction only at one face of the prism b. Emerges out from the prism in a direction parallel to the incident ray c. Bends at both the surfaces of prism towards its base...

### The diagram below shows two identical prisms A and B placed with their faces parallel to each other. A ray of light of single colour PQ is incident at the face of the prism A. Complete the diagram to show the path of the ray till it emerges out of the prism B

Solution :

**A ray of light is normally incident on one face of an equilateral glass prism. Answer the following**

(a)What is the angle of incidence on the first face of the prism? (b)What is the angle of refraction from the first face of the prism? (c)What will be the angle of incidence at the second face of...

**An object is viewed through a glass prism with its vertex pointing upwards. Draw a ray diagram to show the formation of its image seen by the observer.**

Solution: Allow two rays OA and OL from a light source O to collide with the prism. They are refracted along AB and LM, respectively, from the prism's first face. These two rays refract off the...

**How does the angle of deviation depend on refracting angle of the prism?**

Solution: The angle of deviation (????) grows as the angle of prism (A) increases.

**Which of the two prisms, A made of crown glass and B made of flint glass, deviate a ray of light more?**

Solution: The refractive index of the B constructed of flint glass is greater. As a result, B constructed of flint glass deviates a light beam more.

**Name the colour of white light which is deviated (i) the most, (ii) the least, on passing through a prism.**

Solution: Violet colours diverge the greatest when passing through a prism, whereas red colours stray the least.

**A light ray of yellow colour is incident on an equilateral glass prism at an angle of incidence equal to 48**^{o} and suffers minimum deviation by an angle of 36^{o}. (i) What will be the angle of emergence? (ii) If the angle of incidence is changed to (a) 30^{o}, (b) 60^{o}, state whether the angle of deviation will be equal to less than or more than 36^{o}.

^{o}and suffers minimum deviation by an angle of 36

^{o}. (i) What will be the angle of emergence? (ii) If the angle of incidence is changed to (a) 30

^{o}, (b) 60

^{o}, state whether the angle of deviation will be equal to less than or more than 36

^{o}.

Solution: (i) We know that the ray suffers minimum deviation in an equilateral prism. So we can write i1 = i2 Therefore, i2 = 480 (ii) (a) If the incidence angle is increased to 30 degrees ,...

**Draw a ray diagram to show the refraction of a monochromatic ray through a prism when it suffers minimum deviation. How is the angle of emergence related to the angle of incidence in this position.**

Solution: In the equilateral prism, the angle of incidence i1 is equal to the angle of emergence i2 when the prism is in minimum deviation. Therefore, i1 = i2 = i

**A ray of light incident at an angle of incidence i**_{1} passes through an equilateral glass prism such that the refracted ray inside the prism is parallel to its base and emerges at an angle of emergence i_{2}.

_{1}passes through an equilateral glass prism such that the refracted ray inside the prism is parallel to its base and emerges at an angle of emergence i

_{2}.

(a) How is the angle of emergence ‘i2‘ related to the angle of incidence ‘i1‘. (b) What can you say about the angle of deviation in such a situation? Solution: (i) The relation between the angle of...

**Write a relation for the angle of deviation (**????**) for a ray of light passing through an equilateral prism in terms of angle of incident (i), angle of emergence (e), angle of prism (A).**

Solution: For a beam of light travelling through an equilateral prism, the angle of incidence (i) angle of emergence (e), angle of prism (A), and angle of deviation ( ???? ) are related as follows:...

**How does the angle of minimum deviation produced by a prism change with increase in (i) the wavelength of incident light and (ii) the refracting angle of the prism?**

Solution: I The angle of deviation decreases as the wavelength of incident light increases. (ii) As the refracting angle of the prism increases, so does the angle of deviation.

**How does the deviation produced by a prism depend on**

(i) the refraction index of its material, and (ii) the wavelength of incident light Solution: (i) For a given angle of incidence, a prism with a higher refractive index produces a bigger...

**State whether the following statement is ‘true’ or ‘false’.**

The deviation produced by a prism is independent of the angle of incidence and is same for all the colors of light. Solution: False. The angle of deviation decreases at initially, then increases as...

**a) How does the angle of deviation produced by a prism change with increase in the angle of incidence. Draw a curve showing the variation in the angle of deviation with the angle of incidence at a prism surface.**

(b) Using the curve in part (a) above, how do you infer that for a given prism, the angle of minimum deviation δmin is unique for the given light. Solution: Dependence of angle of deviation...

**What do you understand by the deviation produced by a prism? Why is it caused? State three factors on which angle of deviation depends.**

Solution: The ray of light in a prism is refracted by two sloped sides. The prism causes one deviation on the first surface and another on the second surface. As a result, a prism causes a deviation...

**Complete the following sentence:**

The angle of deviation is the angle formed by the ____________ with the direction of ___________. Solution: The angle of deviation is the angle formed by the emergent ray with the direction of...

**Define the term angle of deviation.**

Solution: The angle of deviation is the angle formed by the incident ray's direction and the emergent ray's direction.

### The diagrams (a) and (b) in Fig. below show the refractions of a ray of light of single colour through a prism and a parallel-sided glass and prism, respectively.

(a) In each diagram, label the incident, refracted, emergent rays and the angle of deviation. (b) In what way the direction of emergent ray in the two cases differ with respect to the incident...

**With the help of a diagram of a prism, indicate its refracting surfaces, refracting angle and base.**

Solution: A prism is a transparent material with a triangular cross section surrounded by five plane surfaces.

**A ray of light of wavelength 5400 Angstrom suffers refraction from air to glass. Taking **_{a}μ_{g}** = 3/2, find the wavelength of light in glass.**

_{a}

Given, According to the question, wavelength of light in air is 5400 A0 And the refractive index of glass with respect to air is, aμg = 3 / 2 where a is for air and g is for glass So, using the...

**The refractive index of water with respect to air is 4/3. What is the refractive index of air with respect to water?**

Solution: According to the question, the refractive index of water with respect to air is air μwater = 4 / 3 We can easily determine the refractive index of air with respect to water in the...

**The speed of light in diamond is 125,000 km s**^{-1}. What is the refractive index? (speed of light in air = 3 x 10^{8} m s^{-1}).

^{-1}. What is the refractive index? (speed of light in air = 3 x 10

^{8}m s

^{-1}).

Solution: Given, According to the question, speed of light in diamond is = 125,000 km s-1 Or, = 125 × 106 m / s We know that the speed of light in air is c = 3 × 108 m / s We have to find the...

**The speed of light in air is 3 x 10**^{8} m s^{-1}. Calculate the speed of light in glass. The refractive index of glass is 1.5.

^{8}m s

^{-1}. Calculate the speed of light in glass. The refractive index of glass is 1.5.

Solution: Given According to the question, speed of light in air is c = 3 × 108 m / s And the refractive index of glass is μ = 1.5 We have to calculate the speed of light in glass, v Using the...

**The highest refractive index is of:**

a. Glass b. Water c. Diamond d. Ruby Solution: The correct option is (c) - Diamond. Diamond has the greatest refractive index, with a value of 2.42.Glass has a refractive index...

**How does the refractive index of a medium depend on its temperature?**

Solution: The refractive index of a medium drops as the temperature of the medium rises. With a rise in temperature, the speed of light in that medium increases. As a result, the refractive index =...