Question

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

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

Answer 1

Answer: (A)

According to given figure,
Applying $KVL$ in loop $(i)$
$500I_1+R(I_1-I_2)=12$
$(500+R)I_1-R{I}_2=12\dots (i)$
Applying $KVL$ in loop (ii), we have
$R(I_2-I_1)=-2$
$R{I}_2=R{I}_1-2\dots (ii)$
From Eqs. $(i)$ and $(ii)$, we get
$(500+R)I_1-(R{I}_1-2)=12$
$500I_1+R{I}_1-R{I}_1+2=12$
$500I_1=10$
$I_1=\frac{1}{50}$
From Eq. (ii),
$R{I}_2=R\times \frac{1}{50}-2$
But given that galvanometer $G$ shows zero deflection, hence $I_2=O$
$\therefore 0=\frac{R}{50}-2$
$\frac{R}{50}=2$
$R=100\Omega$