Question

In the meter bridge circuit shown, the null point is obtained at $C(AC=x)$ on the wire AB. If the diameter of the wire AB is doubled, the position of the new null point C will correspond to:

• A. $A{C}^{\prime }=x/2$
• B. $A{C}^{\prime }=x/4$
• C. $A{C}^{\prime }=4x$
• D. $A{C}^{\prime }=x$

Answer 1

Answer: (D)

$A{C}^{\prime }=x$

Let known and unknown resistances be $r_1$ and $r_2$, and the resistance of metre wire be$R$.

$\frac{r_1}{r_2}=\frac{Rx}{R(1-x)}$

Now, after the diameter is doubled,

New resistance of metre wire=$4R$.

Let null point be $A{C}^{\prime }=y$,

$\frac{r_1}{r_2}=\frac{4Ry}{4R(1-y)}$

Comparing with the previous equations,

$y=A{C}^{\prime }=x$

Option $\text{D}$ is the correct answer.