First slide

Kirchoff's Law

Question

What should be value of E for which galvanometer shows no deflection:

Moderate

A

10 V
B

5 V
C

15 V
D

20 V

Solution

If reading of G is Zero, then current through $20 Ω$ is zero. So voltage access $20 Ω$ is zero.
Current in left circuit $i_{1} = \frac{20}{5 + 10 + 5} = 1 A$

current through the right circuit $i_{2} = \frac{e f f e c t i v e e m f}{e f f e c t i v e r e s i s \tan c e} = \frac{10 - E}{20}$
Let say point A is at 0V. Then $V_{D} = 0 V, V_{B} = 10 V, V_{C} = 10 V$
Using KVL,
$V_{C} - 5 i_{2} - E = 0$
$\begin{array}{l} \Rightarrow 10 - 5 (\frac{10 - E}{20}) - E = 0 \\ ∴ E = 10 V \end{array}$

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