Question

A resistance $\text{R}$ is to be measured using a meter bridge. A student chooses the standard resistance $\text{S}$ to be $100\Omega$. He finds the null point at $l_1=2.9\text{cm}$. He is told to attempt to improve the accuracy. Which of the following is a useful way ?

• A. He should measure $l_1$ more accurately
• B. He should change $S$ to $1000\Omega$ and repeat the experiment
• C. He should change $S$ to $3\Omega$ and repeat the experiment
• D. He should give up hope of a more accurate measurement with a meter bridge

Answer 1

The correct option is C He should change $S$ to $3\Omega$ and repeat the experiment

The percentage error in $\text{R}$ can be minimized by adjusting the balance point near the middle of the bridge, i.e., when $l_1$ is close to $50\text{cm}$.
This requires a suitable choice of $\text{S}$.

For balanced bridge

$\frac{R}{S}=\frac{l_1}{(100-l_1)}=\frac{2.9}{100-2.9}$

Since, $R:S::2.9:97.1$ imply that the $S$ is nearly 33 times to that of $R$.

In order to make this ratio $1:1$, it is necessary to reduce the value of $S$ nearly $\frac{1}{33}$ times i.e., nearly $3\Omega$.

So, option $\left(c\right)$ is correct.