During an experiment with a metre bridge, the galvanometer shows a null point when the jockey is pressed at $40.0 cm$ using a standard resistance of $90 \Omega$, as shown in the figure. The least count of the scale used in the metre bridge is 1 $mm$. The unknown resistance is

JEE Advanced · 2014 · 25 May 2014 · Paper 2 · Current Electricity

During an experiment with a metre bridge, the galvanometer shows a null point when the jockey is pressed at

40.0 c m

using a standard resistance of

90Ω

, as shown in the figure. The least count of the scale used in the metre bridge is 1

mm

. The unknown resistance is

(A) $60 \pm 0.15Ω$
(B) $135 \pm 0.56Ω$
(C) $60 \pm 0.25Ω$ ✓ Correct
(D) $135 \pm 0.23Ω$

Answer: (C)

Solution

Using the metre bridge balance condition:

\frac{R}{40} = \frac{90}{60}

, so

R = 60Ω

.

For error calculation:

\frac{Δ R}{R} = \frac{Δ ℓ _{1}}{ℓ _{1}} + \frac{Δ ℓ _{2}}{ℓ _{2}} = \frac{0.1}{40} + \frac{0.1}{60} = \frac{5}{1200} = \frac{1}{240}

.

Therefore,

Δ R = \frac{R}{240} = \frac{60}{240} = 0.25Ω

.

The unknown resistance is

60 \pm 0.25Ω

JEE Advanced · 2014 · 25 May 2014 · Paper 2 · Single correct option

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