Question

Figure shows a potentiometer with length of wire $1\text{m}$ and resistance $10\Omega$. In this system, find length $l$ when galvanometer shows null deflection.

• A. $40.5\text{cm}$
• B. $37.5\text{cm}$
• C. $35.5\text{cm}$
• D. $43.5\text{cm}$

Answer 1

The correct option is B $37.5\text{cm}$


Current in the loop $1$ of the above potentiometer is,

$i_1=\frac{2}{10+15}=\frac{2}{25}\text{A}$

Similarly, in loop $2$,

$i_2=1\text{A}$

Now, the potential gradient in the wire is given as,
$\lambda =\frac{V_{PQ}}{100}=\frac{\frac{2}{25}\times 10}{100}=\frac{1}{125}\text{V/cm}$

From figure,

$V_{PR}=V_{ST}$

$\Rightarrow -\lambda l=1.2i_2-1.5$

$\Rightarrow -\frac{1}{125}\times l=1.2\times 1-1.5$

$\Rightarrow l=37.5\text{cm}$

Hence, option $\left(B\right)$ is the correct answer.