Question

In the circuit shown E, F, G and H are cells of emf 2, 1, 3 and 1 V and their internal resistances are 2, 1, 3 and 1 $\Omega$ respectively. Calculate the potential difference between B and D :

• A. $\frac{1}{13}V$
• B. $\frac{2}{13}V$
• C. $\frac{3}{13}V$
• D. $\frac{10}{13}V$

Answer 1

Answer: (B)

$\frac{2}{13}V$

Applying KVL for

loop BADB: $2-1=2I+I+2(I-I^{\prime })$ or $1=5I-2I^{\prime }.....\left(1\right)$

and for loop DCBD: $3-1=3I^{\prime }+I^{\prime }-2(I-I^{\prime })$ or $2=6I^{\prime }-2I....\left(2\right)$

Solving (1) and (2) we get, $I=\left(5/13\right)A,I^{\prime }=\left(6/13\right)A$

The potential difference between B and D is $V_{bd}=-2(I-I^{\prime })=-2(5/13-6/13)=2/13V$