Resistances in two gaps of a metre bridge are \( 8\,\Omega \) and \( 24\,\Omega \), respectively. The distance by which the balance point shifts by interchanging the resistances in the two gaps, is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 50 cm
A metre bridge is balanced when the ratio of the resistances in the gaps equals the ratio of the two lengths of wire, measured from the left end to the balance point and from there to the right end.
\( \displaystyle \frac{R_1}{R_2} = \frac{l}{100 - l} \)
Before the interchange (\( R_1 = 8\,\Omega,\ R_2 = 24\,\Omega \)):
\( \displaystyle \frac{l_1}{100 - l_1} = \frac{8}{24} = \frac{1}{3} \;\Rightarrow\; 3l_1 = 100 - l_1 \;\Rightarrow\; l_1 = 25\,\mathrm{cm} \)
After the interchange (\( R_1 = 24\,\Omega,\ R_2 = 8\,\Omega \)):
\( \displaystyle \frac{l_2}{100 - l_2} = 3 \;\Rightarrow\; l_2 = 75\,\mathrm{cm} \)
\( \displaystyle \text{shift} = l_2 - l_1 = 75 - 25 = 50\,\mathrm{cm} \)