Question

In the circuit, the galvanometer $ G $ shows zero deflection. If the batteries $ A $ and $ B $ have negligible internal resistance, the value of the resistor $ R $ will be

• A. $ 200 \,Ω $
• B. $ 100 \,Ω $
• C. $ 500 \,Ω $
• D. $ 1000 \,Ω $

Answer 1

Answer: (B)

The galvanometer shows zero deflection ie, current through $XY$ is zero.

As a result potential drop across $R$ is $2 \,V$, circuit can be redrawn as

$I=\frac{12}{500+R}$
Voltage across $R$, $V=IR$
$\Rightarrow 2=\frac{12}{500+R}\times R$
$\Rightarrow 1000+2R=12R$
$\Rightarrow R=100\,\Omega$