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. $200\Omega$
• B. $100\Omega$
• C. $500\Omega$
• D. $1000\Omega$

Answer 1

Answer: (B)

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

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

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