Question

A meter 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 a $52cm$ mark. The end-corrections are $1cm$ and $2cm$ respectively for the ends A and B. The determined value of X is

• A. $10.2\Omega$
• B. $10.6\Omega$
• C. $10.8\Omega$
• D. $11.1\Omega$

Answer 1

The correct option is B

$10.6\Omega$

Step 1. Given data:

Resistance = $10$ohm

Tapping key initial mark = $52cm$

End-corrections at A and B = $1cm$ and $2cm$ respectively.

Step 2. Finding unknown resistance:

Applying the condition of the balanced Wheatstone bridge, we get

$$\begin{gathered} \frac{X}{10}=\frac{\left(52+1\right)}{\left(\left(100-52\right)+2\right)}=\frac{53}{50} \\ X=\frac{53}{50}\times 10=10.6\Omega \end{gathered}$$

Thus, the correct option is option B.