In a meter bridge experiment to determine the value of unknown resistance, first the resistances $2\Omega$ and $3\Omega$ are connected in the left and right gaps of the bridge and the null point is obtained at a distance $l$ cm from the left. Now when an unknown resistance $x\Omega$ is connected in parallel to $3\Omega$ resistance, the null point is shifted by 10 cm to the right of wire. The value of unknown resistance $x$ is
______ $\Omega$.
Numerical value type. Enter your answer.
Answer: 6
First balance: $\dfrac23 = \dfrac{l}{100 - l}\Rightarrow l = 40$ cm.
New null point at $50$ cm, so the right gap now equals the left gap:
$$\frac{2}{R_{\text{right}}} = \frac{50}{50}\Rightarrow R_{\text{right}} = 2\ \Omega$$
$$\frac{3x}{3 + x} = 2\Rightarrow 3x = 6 + 2x\Rightarrow x = 6\ \Omega$$
Solution by Sreeraj P, M.Sc Physics