A metre bridge is set up as shown, to determine an unknown resistance $' X'$ using a standard 10 ohm resistor. The galvanometer shows null point when tapping-key is at 52 cm mark. The end-corrections are 1 cm and 2 cm respectively for the ends A and B. The determined value of $' X'$ is [2011]

Question

Smart Achievers · Accepted Answer

(2)

Applying balanced Wheatstone bridge condition $\frac{P}{Q} = \frac{R}{S}$

$\frac{X}{ℓ_{1}} = \frac{10}{ℓ_{2}}$

$Here ℓ_{1} = 52 + end correction = 52 + 1 = 53 cm$

$ℓ_{2} = 48 + end correction = 48 + 2 = 50 cm$

or $\frac{X}{53} = \frac{10}{50}$ $∴$ $X = \frac{53 \times 10}{50} = \frac{53}{5} = 10.6 Ω$

Solution

Q.
A metre bridge is set up as shown, to determine an unknown resistance $' X'$ using a standard 10 ohm resistor. The galvanometer shows null point when tapping-key is at 52 cm mark. The end-corrections are 1 cm and 2 cm respectively for the ends A and B. The determined value of $' X'$ is [2011]

1 10.2 ohm

2 10.6 ohm

3 10.8 ohm

4 11.1 ohm

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