In an experiment with Meter Bridge, with unknown resistance R in the left gap, the null point is obtained at 40 cm from the left end. Now a resistance of \( 10\,\Omega \) is connected in series with resistance R, the null point is obtained at 70 cm from the left end. The value of resistance R is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( 4\,\Omega \)
A meter bridge is a Wheatstone bridge. At the null point, the ratio of the two resistances in the gaps equals the ratio of the two lengths of the wire.
\( \displaystyle \frac{R}{S} = \frac{l}{100 - l} \)
Let \( S \) be the resistance in the right gap. First balance, \( l = 40\,\mathrm{cm} \):
\( \displaystyle \frac{R}{S} = \frac{40}{60} \;\Rightarrow\; S = 1.5R \)
Second balance, with \( R + 10 \) in the left gap and \( l = 70\,\mathrm{cm} \):
\( \displaystyle \frac{R + 10}{S} = \frac{70}{30} \;\Rightarrow\; R + 10 = \frac{7}{3} \times 1.5R = 3.5R \)
\( \displaystyle 2.5R = 10 \;\Rightarrow\; R = 4\,\Omega \)
(The right gap then holds \( S = 6\,\Omega \).)