Question

In the circuit shown in Figure E, F, G and H are cells of emf 2, 1, 3, and 1 V, respectively. The resistance $2\Omega ,1\Omega ,3\Omega$, and $1\Omega$ are their respective internal resistances. If the potential difference between G and H is $\frac{7x}{13}V$. Find $x$

Answer 1

Applying KVL
for loop ADBA: $2-1=I+2(I-I^{\prime })+2I$ or $5I-2I^{\prime }=1....\left(1\right)$
for loop DCBD: $3-1=-I^{\prime }-3I^{\prime }+2(I-I^{\prime })$ or $2I-6I^{\prime }=2....\left(2\right)$
Solving (1) and (2), we get $I=5/13,I^{\prime }=6/13$
Potential across the terminal of cell G is $V_G=3-3I^{\prime }=3-(3\times 6/13)=21/13V$