Question

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

• A. $45.50cm$
• B. $56.87\text{ c}m$
• C. $36.40cm$
• 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.
$\Rightarrow \frac{5}{4}=\frac{45.5}{L_2}$
$\Rightarrow L_2=\frac{45.5\times 4}{5}$
$\Rightarrow L_2=36.4cm$