Question

A battery of emf $\varepsilon_{0}=12 \,V$ is connected across a $4 \,m$ long uniform wire having resistance $4 \,\Omega / m$ The cells of small emfs $\varepsilon_{1}=2 \,V$ and $\varepsilon_{2}=4 \,V$ having internal resistance $2\, \Omega$ and $6 \,\Omega$, respectively, are connected as shown in the figure. If galvanometer shows no deflection at the point $N$, the distance of point $N$ from the point $A$ is equal to

• A. $\frac{1}{6} m$
• B. $\frac{1}{3} m$
• C. 25 cm
• D. 50 cm

Answer 1

Answer: (C)

Potential gradient,
$x=\left(\frac{12}{8+16}\right) \times 4=2 \,Vm ^{-1}$
Effective emf of $E_{1}$ and $E_{2}$
$E=\frac{\frac{E_{1}}{r_{1}}-\frac{E_{2}}{r_{2}}}{1 / r_{1}+1 / r_{2}}=\frac{1}{2} \text { volt }$
Balancing length $=\left(\frac{1}{2}\right)\left(\frac{1}{2}\right)=\frac{1}{4} m =25 \,cm$