First slide

KVL

Question

In the circuit shown in fig. E, F, G and H are cells of e.m.f. 2, 1, 3 and 1 volt and their internal resistances
are 2, 7,3 and 1 ohm respectively. The potential difference between B and D is

Moderate

A

(2/13) v
B

(3/13) v
C

(5/13) V
D

zero

Solution

shows the current distribution
Applying Kirchhoff's first law at point D, we have
$i = i_{1} + i_{2}$ …………(1)
Applying Kirchhoff second law to mesh,DBA, we have
$2 i + 1 i + 2 i_{1} = 2 - 1 = 1$
or $3 i + 2 i_{1} = 1$ ……..(2)
Applying Kirchhoff second law to mesh DCBD we get
$3 i_{2} + 1 i_{2} - 2 i_{1} = 3 - 1$
or $4 i_{2} - 2 i_{1} = 2$ …….(3)
Solving eqs. (1), (2) and (3), we get
$i_{1} = - \frac{1}{13} amp ., i_{2} = \frac{6}{13} amp . and i = \frac{5}{13} amp .$
Potential difference between B and D
$= 2 i_{1} = 2 (\frac{1}{13}) = \frac{2}{13} volt$

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