Question

Resistance in the two gaps of a metre bridge are $15\Omega$ and $45\Omega$ respectively. If the resistances are interchanged, the balance point shifts by

• A. $50\text{cm}$
• B. $25\text{cm}$
• C. $40\text{cm}$
• D. $20\text{cm}$

Answer 1

The correct option is B $25\text{cm}$

Case $\left(i\right)$
$\frac{R_1}{R_2}=\frac{l}{100-l}\Rightarrow \frac{15}{45}=\frac{l}{100-l}\Rightarrow 100-l=3l$
$4l=100$
$l=25\text{cm}$

Case $\left(ii\right)$
After interchanging
$\frac{R_2}{R_1}=\frac{l_1}{100-l_1}\Rightarrow \frac{45}{15}=\frac{l_1}{100-l_1}$
$3(100-l_1)=l_1$
$300=4l_1$
$l_1=\frac{300}{4}=75\text{cm}$

Shift in balance point is $=l_1-l=75-25=50\text{cm}$.