In a meter bridge, the null point is found at a distance of 60 cm from end A. If a 5 Ω resistor is now connected in series with S, the null point occurs at 50 cm. The values of R and S are, respectively
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 15 Ω and 10 Ω
At the null point of a meter bridge the bridge is balanced. R is in the left gap, on the side of end A, so the balancing length \( l \) is measured from A on R's side and the balance condition is
\( \displaystyle \frac{R}{S} = \frac{l}{100 - l} \)
First balance, \( l = 60\,\mathrm{cm} \):
\( \displaystyle \frac{R}{S} = \frac{60}{40} \;\Rightarrow\; R = 1.5\,S \)
With \( 5\,\Omega \) in series with S, \( l = 50\,\mathrm{cm} \):
\( \displaystyle \frac{R}{S + 5} = \frac{50}{50} = 1 \;\Rightarrow\; R = S + 5 \)
\( \displaystyle 1.5\,S = S + 5 \;\Rightarrow\; S = 10\,\Omega \)
\( \displaystyle R = 1.5 \times 10 = 15\,\Omega \)