First slide

potentiometer

Question

In the arrangement shown in figure, when the switch S₂ is open, the galvanometer shows no deflection for $l = \frac{L}{2} .$ When the switch S₂ is closed, the galvanometer shows no deflection for $l = \frac{5 L}{12} .$ The internal resistance (r) of 6 V cell, and the emf E of the other battery are respectively

Moderate

A

$3 Ω, 8 V$
B

$2 Ω, 12 V$
C

$2 Ω, 24 V$
D

$3 Ω, 12 V$

Solution

When S₂ open:
Assume resistance of AB = R
Resistance of wire per unit length, $x = \frac{R}{L}$
$I = \frac{E}{R}$
Now for null point at $l = \frac{L}{2}$
$\frac{E}{R} \times \frac{R}{L} \times \frac{L}{2} = 6$
E = 12 V
$\begin{array}{l} V_{1} = \frac{E}{R} \times \frac{R}{L} \times \frac{5 L}{12} = \frac{5 \times 12}{12} = 5 V \\ \Rightarrow 6 - I_{1} r = 5 \Rightarrow 6 - (\frac{5}{10}) r = 5 \Rightarrow r = 2 Ω \end{array}$

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