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)

$100\,\Omega$

Answer 2

The galvanometer shows zero deflection, i.e., 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 $R, V = IR$ $\Rightarrow 2=\frac{12}{500+R}\times R$ $\Rightarrow 1000 + 2R = 12R \Rightarrow R=100\,\Omega$