Question

A meter bridge is set-up as shown in figure, to determine an unknown resistance $X$ using a standard $10 \Omega$ 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

• A. $10 \Omega$
• B. $10.6 \Omega$
• C. $10.8 \Omega$
• D. $11.1 \Omega$

Answer 1

Answer: (B)

$10.6 \Omega$

Answer 2

Using the concept of balanced Wheat stone bridge, we have,
$\, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \frac{P}{Q} = \frac{R}{S}$
$\therefore \, \, \, \, \, \, \, \, \, \, \frac{X}{(52 + 1)} = \frac{10}{(48 + 2)}$
$\therefore \, \, \, \, \, \, \, X = \frac{10 \times 53}{50} = 10.6 \Omega$
$\therefore$ Correct option is (b).