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

Question

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Answer 1

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

Answer 2

Applying KVL
for loop ADBA:

2 - 1 = I + 2 (I - I^{'}) + 2 I

or

5 I - 2 I^{'} = 1 . . . . (1)

for loop DCBD:

3 - 1 = - I^{'} - 3 I^{'} + 2 (I - I^{'})

or

2 I - 6 I^{'} = 2 . . . . (2)

Solving (1) and (2), we get

I = 5 / 13, I^{'} = 6 / 13

Potential across the terminal of cell G is

V_{G} = 3 - 3 I^{'} = 3 - (3 \times 6 / 13) = 21 / 13 V