Physics

A magnetic field B is confined to a region r a ≤ and points out of the paper (the z-axis), r = 0 being the centre of the circular region. A charged ring (charge = Q) of radius b, b > a and mass m lies in the x-y plane with its centre at the origin. The ring is free to rotate and is at rest. The magnetic field is brought to zero in time ∆t. Find the angular velocity ω of the ring after the field vanishes.

When the magnetic field is lowered in t, the magnetic flux across the conducting ring drops to zero from its maximum. E2b = induced emf According to Faraday's law of emf, The induced emf is equal to...

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A rectangular loop of wire ABCD is kept close to an infinitely long wire carrying a current II ( ) t = o (1– /t T ) for 0 ≤ ≤ t T and I (0) = 0 for t > T. Find the total charge passing through a given point in the loop, in time T. The resistance of the loop is R.

If the instantaneous current is t, then I(t) = 1/R d/dt I(t) If q is the charge that passes during time t, dQ/dt = I(t) 1/R d/dt = dQ/dt When we integrate the equation, we obtain Q = 0L1L2/2R log...

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i) When the position of the rotating conductor is assumed to be at the time interval t = 0 to t = π/4ꞷ We get current I = 1/2 Bl2ꞷ/λl sec2 ꞷt cos ꞷt = Blꞷ/2λ cos ꞷt ii) When the position of the rotating conductor is at time interval π/4ꞷ < t < 3π/4ꞷ We get current I = 1/2 Blꞷ/λ sin ꞷt iii) When the position of the rotating conductor is at time interval 3π/4ꞷ < t < π/ꞷ We get current I = 1/2 Blꞷ/ λ sin ꞷt

I If the spinning conductor's location is considered to be in the time period t = 0 to t = 4 We obtain current I = 1/2 Bl2/l sec2 t cos t = Bl/2 cos t = Bl/2 cos t = Bl/2 cos t = Bl/2 cos t = Bl/2...

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A conducting wire XY of mass m and negligible resistance slides smoothly on two parallel conducting wires. The closed-circuit has a resistance R due to AC. AB and CD are perfect conductors. There is a magnetic field B = B t(k ). (i) Write down the equation for the acceleration of the wire XY. (ii) If B is independent of time, obtain v(t) , assuming v (0) = u0. (iii) For (b), show that the decrease in kinetic energy of XY equals the heat lost in R.

m = B.A = BA cos m The area vector is A, while the magnetic field vector is B. e1 = -dB(t)/dt lx e1 e2 = B(t) lv (t) The total emf in the circuit is equal to the emf owing to field change plus the...

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A magnetic field B = Bo sin ωt k covers a large region where a wire AB slides smoothly over two parallel conductors separated by a distance d. The wires are in the x-y plane. The wire AB (of length d) has resistance R and the parallel wires have negligible resistance. If AB is moving with velocity v, what is the current in the circuit? What is the force needed to keep the wire moving at constant velocity?

Allow wire AB to travel with velocity v at time t = 0. x(t) = vt at time t AB = e1 = Blv Motional emf across (Bo sin t)vd = e1 (-j) d(B)/dt = e2 e2 = -B0 cos tx (t)d e2 = -B0 cos tx (t)d e2 = -B0...

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There are two coils A and B separated by some distance. If a current of 2 A flows through A, a magnetic flux of 10-2 Wb passes through B (no current through B). If no current passes through A and a current of 1 A passes through B, what is the flux through A?

The current flowing through the coil is denoted by Ia. Mutual induction between A and B is known as Mab. The number of turns in coil A is Na. The number of turns in coil B is Nb. an is the flux...

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A (current vs time) graph of the current passing through a solenoid is shown in Fig 6.9. For which time is the back electromotive force (u) a maximum. If the back emf at t = 3s is e, find the back emf at t = 7 s, 15s and 40s. OA, AB and BC are straight line segments.

We may deduce from the graph that when the rate of change of magnetic flux reaches its highest, the electromagnetic force, which is proportional to the rate of change of current, reaches its...

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Find the current in the wire for the configuration. Wire PQ has negligible resistance. B, the magnetic field is coming out of the paper. θ is a fixed angle made by PQ travelling smoothly over two conducting parallel wires separated by a distance d.

F is the force acting on PQ's free charge particle. The motional emf is calculated by multiplying E along the PQ by the effective length of the PQ. As a result, the induced current will be vBd/R,...

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Consider a closed loop C in a magnetic field such that the flux passing through the loop is defined by choosing a surface whose edge coincides with the loop and using the formula φ= B1dA1 + B2dA2 + …. Now if we chose two different surfaces S1 and S2 having C as their edge, would we get the same answer for flux. Justify your answer.

The magnetic flux lines that pass through are identical to those that flow through the surface. The magnetic field lines in an area A with magnetic flux B are represented by = B1dA1 + B2dA2. As a...

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A magnetic field in a certain region is given by B = Bo cos ωt k and a coil of radius a with resistance R is placed in the x-y plane with its centre at the origin in the magnetic field. Find the magnitude and the direction of the current at (a, 0, 0) at t =π ω /2, t =π /2ω and t =3π/ω

The magnetic field is directed along the z-axis. B.A = BA cos = B.A cos = B.A cos = B.A cos = B.A cos Using the electromagnetic induction law of Faraday, R sin t = Boa2/R sin t = I = Boa2/R sin t =...

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Consider a metallic pipe with an inner radius of 1 cm. If a cylindrical bar magnet of radius 0.8cm is dropped through the pipe, it takes more time to come down than it takes for a similar unmagnetised cylindrical iron bar dropped through the metallic pipe. Explain.

The magnetic flux across the pipe changes when a cylindrical bar magnet with a radius of 0.8 cm is dropped through it, causing eddy currents to form. The existence of eddy current causes the magnet...

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Consider a metal ring kept (supported by a cardboard) on top of a fixed solenoid carrying a current I. The centre of the ring coincides with the axis of the solenoid. If the current in the solenoid is switched off, what will happen to the ring?

We already know that current was flowing through the solenoid, causing it to act like a magnet with the S pole on the upper side. As a result, the ring has no induced current. When the current is...

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A circular coil expands radially in a region of the magnetic field and no electromotive force is produced in the coil. This can be because (a) the magnetic field is constant. (b) the magnetic field is in the same plane as the circular coil and it may or may not vary. (c) the magnetic field has a perpendicular (to the plane of the coil) component whose magnitude is decreasing suitably. (d) there is a constant magnetic field in the perpendicular (to the plane of the coil) direction.

(b) the magnetic field is in the same plane as the circular coil and it may or may not vary. (c) the magnetic field has a perpendicular (to the plane of the coil) component whose magnitude is...

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An e .m.f is produced in a coil, which is not connected to anexternal voltage source. This can be due to (a) the coil is in a time-varying magnetic field. (b) the coil moving in a time-varying magnetic field. (c) the coil moving in a constant magnetic field. (d) the coil is stationary in an external spatially varying magnetic field, which does not change with time.

(a) the coil is in a time-varying magnetic field. (b) the coil moving in a time-varying magnetic field. (c) the coil moving in a constant magnetic field.

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A metal plate is getting heated. It can be because (a) a direct current is passing through the plate. (b) it is placed in a time-varying magnetic field. (c) it is placed in a space varying magnetic field, but does not vary with time. (d) a current (either direct or alternating) is passing through the plate.

(a) The plate is receiving a direct current. (b) it is exposed to a magnetic field that changes over time. (c) it is put in a magnetic field that varies in space but not in time.

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There are two coils A and B. A current starts flowing in B as shown, when A is moved towards B and stops when A stops moving. The current in A is counterclockwise. B is kept stationary when A moves. We can infer that (a) there is a constant current in the clockwise direction in A. (b) there is a varying current in A. (c) there is no current in A. (d) there is a constant current in the counterclockwise direction in A.

(d) In A, there is a counterclockwise current that is constant.

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A cylindrical bar magnet is rotated about its axis. A wire is connected from the axis and is made to touch the cylindrical surface through a contact. Then (a) a direct current flows in the ammeter A. (b) no current flows through the ammeter A. (c) an alternating sinusoidal current flows through the ammeter A with a time period T=2π/ω. (d) a time-varying non-sinusoidal current flows through the ammeter A.

(b) There is no current flowing through ammeter A.

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A thin circular loop of radius R rotates about its vertical diameter with an angular frequency ω. Show that a small bead on the wire loop remains at its lowermost point for ω ≤ √g / R . What is the angle made by the radius vector joining the centre to the bead with the vertically downward direction for ω = √2g/ R ? Neglect friction.

Let θ be the angle made by the radius vector joining the bead and the centre of the wire with the downward direction. Let, N be the normal reaction mg = N cosθ —–(1) mrω2 = Nsinθ —– (2) (or) m...

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The rear side of a truck is open and a box of 40 kg mass is placed 5 m away from the open end as shown in Fig. The coefficient of friction between the box and the surface below it is 0.15. On a straight road, the truck starts from rest and accelerates with 2 ms-2. At what distance from the starting point does the box fall off the truck? (Ignore the size of the box).

F = ma = 40 x 2 = 80 N is the force experienced by the box. Ff = mg = 0.15 x 40 x 10 = 60 N Frictional force F – Ff = 80 – 60 = 20 N Net force = F – Ff = 80 – 60 = 20 N In the box, a =20/40(Net...

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A block of mass 15 kg is placed on a long trolley. The coefficient of static friction between the block and the trolley is 0.18. The trolley accelerates from rest with 0.5 ms-2 for 20 s and then moves with uniform velocity. Discuss the motion of the block as viewed by (a) a stationary observer on the ground, (b) an observer moving with the trolley.

The block's mass is 15 kg. Static friction coefficient between the block and the trolley, p= 0.18 The trolley accelerates at a rate of 0.5 m/s2. (a) The force experienced by the block, F = ma = 15 x...

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Figure shows a man standing stationary with respect to a horizontal conveyor belt that is accelerating with 1 ms-2. What is the net force on the man? If the coefficient of static friction, between the man’s shoes and the belt is 0.2, up to what acceleration of the belt can the man continue to be stationary relative to the belt? (Mass of the man = 65 kg.)

Here, the conveyor belt's acceleration is a = 1 ms-2. s=0.2 is the static friction coefficient. m = 65 kg m = 65 kg m = 65 kg m = 65 kg m = 65 kg Ma = 65 x 1 = 65N is the Net Force. The friction...

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A stone of mass 0.25 kg tied to the end of a string is whirled round in a circle of radius 1.5 m with a speed of 40 rev./min in a horizontal plane. What is the tension in the string? What is the maximum speed with which the stone can be whirled around if the string can withstand a maximum tension of 200 N?

The stone weighs 0.25 kilogramme. r = 1.5 m Radius n= 40/60 = (23) rev/sec is the number of revolutions per second. = 2n = 2 x 3.14 x (23) is the angular velocity. The centripetal force is provided...

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Two bodies of masses 10 kg and 20 kg respectively kept on a smooth, horizontal surface are tied to the ends of a tight string. A horizontal force F = 600 N is applied to (i) A, (ii) B along the direction of string. What is the tension in the string in each case?

Given, A body mass of 10 kilogrames (m1) B, m2 = 20 kg, 600 N horizontal force m = m1 + m2 = 30 kg is the total mass of the system. Using Newton's second rule of motion, we can calculate ma = f...

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A truck starts from rest and accelerates uniformly at 2.0 ms-2. At t = 10 s, a stone is dropped by a person standing on the top of the truck (6 m high from the ground). What are the (a) velocity, and (b) acceleration of the stone at t = 11s? (Neglect air resistance.)

u = 0 is the initial velocity. a = 2 ms-2, a = 2 ms-2, a = 2 ms-2, a = 2 m   t=10s t=10s t=10s t=10   We get v = u + at using the equation v = u + at.   20 m/s = v = 0 + 2 x 10  ...

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A body of mass 0.40 kg moving initially with a constant speed of 10 ms-1 to the north is subject to a constant force of 8.0 N directed towards the south for 30 s. Take the instant the force is applied to be t = 0, the position of the body at that time to be x = 0, and predict its position at t = -5 s, 25 s, 100 s.

Given, Body mass is 0.40 kg. u = 10 m/s initial velocity f = -8 N force (retarding force) Using the formula S = ut + (12) at2, (a) At time t = – 5 s, position From t = 0 s, the force acts on the...

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The driver of a three-wheeler moving at a speed of 36 km/h sees a child standing in the middle of the road and brings his vehicle to rest in 4.0 s just in time to save the child. What is the average retarding force on the vehicle? The mass of the three-wheeler is 400 kg, and the mass of the driver is 65 kg.

Given, u=36 km/h is the initial velocity. v = 0 is the final velocity. The three-mass wheeler's is m1=400 kg. The driver's mass is m2 = 65 kg. The time it took to bring the car to a complete stop...

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One end of a string of length l is connected to a particle of mass m and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed v the net force on the particle (directed towards the centre) is : (i) T (ii) T – mv2/l (iii) T + mv2/l (iv) 0 T is the tension in the string. [Choose the correct alternative].

T is the particle's net force, and it is directed towards the centre. It gives the particle the centrifugal force it needs to travel in a circle.

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Give the magnitude and direction of the net force acting on a stone of mass 0.1 kg, (a) just after it is dropped from the window of a stationary train (b) just after it is dropped from the window of a train running at a constant velocity of 36 km/h (c ) just after it is dropped from the window of a train accelerating with1 m s-2 (d) lying on the floor of a train which is accelerating with 1 m s-2, the stone being at rest relative to the train. Neglect air resistance throughout.

(a) Stone mass = 0.1 kg 10 ms^(-2)= acceleration   F = mg = 0.1 x 10 = 1.0 N is the net force.   The force is applied vertically and downwards.   (b) The train maintains a steady...

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A pebble of mass 0.05 kg is thrown vertically upwards. Give the direction and magnitude of the net force on the pebble, (a) during its upward motion (b) during its downward motion (c) at the highest point where it is momentarily at rest. Do your Solutions change if the pebble was thrown at an angle of 45° with the horizontal direction? Ignore air resistance

(a) The acceleration due to gravity acts downwards throughout the upward motion of the pebble, thus the magnitude of the force on the pebble is 0.5 N = F = mg = 0.05 kg x 10 ms-2 The force is in a...

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1. Give the magnitude and direction of the net force acting on (a) a drop of rain falling down with a constant speed (b) a cork of mass 10 g floating on water (c) a kite skillfully held stationary in the sky (d) a car moving with a constant velocity of 30 km/h on a rough road (e) a high-speed electron in space far from all material objects, and free of electric and magnetic fields.

(a)The raindrop continues to fall at the same rate. As a result, the acceleration will be zero. Because F = ma, the force exerted on the drop will be zero when the acceleration is zero. (b) The cork...

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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...

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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 =...

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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...

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(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...

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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 =...

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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...

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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 =...

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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 =...

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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...

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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...

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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.

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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...

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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,...

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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...

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