Find out the following in the electric circuit given in Figure 12.9
(a) Effective resistance of two 8 Ω resistors in the combination
(b) Current flowing through 4 Ω resistor
Find out the following in the electric circuit given in Figure 12.9
(a) Effective resistance of two 8 Ω resistors in the combination
(b) Current flowing through 4 Ω resistor

Solution:

(a) Since, two 8 \Omega resistors are in parallel, then their effective resistance R_{p} is given by

    \[\begin{aligned}\frac{1}{R_{p}} &=\frac{1}{R_{1}}+\frac{1}{R_{2}}=\frac{1}{8}+\frac{1}{8}=\frac{1}{4} \S_{p} &=4 \Omega\end{aligned}\]

b)

Total resistance in the circuit.

    \[R=4 \Omega+R_{p}=4 \Omega+4 \Omega=8 \Omega\]


Current through the circuit,

    \[I=\frac{V}{R}=\frac{8}{8}=1 A\]


Thus, current through 4 \Omega resistor is 1 A as 4 \Omega and R_{p} are in series and same current flows through them.