Question

In the following figure, the p.d. between the points $M$ and $N$ is balanced at $50\text{cm}$. length. The length in $\text{cm}$, balancing for the potential difference between points $N$ and $C$ will be –

• A. $40$
• B. $100$
• C. $75$
• D. $25$

Answer 1

The correct option is B $100$

Suppose the current flowing in the secondary circuit is $I$.
Resistance across $MN=\frac{4.4}{4+4}=2\Omega$
Then, $V_{MN}=I\left(2\Omega \right)=\left(50x\text{cm}\right)$
Since the balancing length is $50x\text{cm}$,
let the balancing length is $L\text{cm}$, this means,
$V_{NC}=I\left(4\Omega \right)=Lx\text{cm}$
$\frac{V_{MN}}{V_{NC}}=\frac{2I}{4I}\Rightarrow \frac{50x}{Lx}=\frac{1}{2}$
This means $L=100\text{cm}$.