Question

In a meter bridge experiment, null point is obtained at $20\text{cm}$ from one end of the wire when resistance $x$ is balanced against resistance $y$. If $x<y$, then where will be the new position of the null point from the same end, if one decides to balance a resistance of $4x$ against $y$ ?

• A. $50\text{cm}$
• B. $80\text{cm}$
• C. $40\text{cm}$
• D. $70\text{cm}$

Answer 1

The correct option is A $50\text{cm}$

The equivalent circuit when the resistances are $x$ and $y$ is given below
For balanced meter bridge
$\frac{x}{20}=\frac{y}{80}$

$\therefore 4x=y$

Applying condition for balanced Wheatstone bridge when the resistances are $4x$ and $y$ is

$\frac{4x}{l_1}=\frac{y}{100-l_1}$

$\frac{1}{l_1}=\frac{1}{100-l_1}(\because 4x=y)$

$l_1=\frac{100}{2}=50\text{cm}$

Therefore, option $\left(a\right)$ is correct.