Question

In a potentiometer arrangement shown in fig. The balancing length for potential difference across $X,Y$ points is found to be $45.5 \, cm$ . Then the balancing length for potential difference across $\left(Y\right)$ and $\left(Z\right)$ would be

• A. $45.50 \, cm$
• B. $56.87\text{ c}m$
• C. $36.40 \, cm$
• D. none of the above

Answer 1

Answer: (C)

Determine the value of potential gradient for the given potentiometer bridge,
And also take ratio of potential drop across both the resistance.
That can be written as,
$\frac{V_{1}}{V_{2}}=\frac{R_{1}}{R_{2}}=\frac{L_{1}}{L_{2}}$ , where $V_{1},V_{2},R_{1},R_{2},L_{1}\&L_{2}$ represents voltage across $5\Omega$ , voltage across $4\Omega$ , value of first resistance, value of second resistance, balancing point for first resistance and balancing point of second resistance respectively.
$\Rightarrow \frac{5}{4}=\frac{45.5}{L_{2}}$
$\Rightarrow L_{2}=\frac{45.5 \times 4}{5}$
$\Rightarrow L_{2}=36.4cm$