A meter bridge is set up as shown

 

Question :- A meter bridge is set up as shown to determine an unknown resistance $X$ using a standard $10ohm$ 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 Ω

(b) 10.6 Ω

(c) 10.8 Ω

(d) 11.1 Ω

Solution :-

Applying end corrections

$l_1=52+1=53cm$
$l_2=48+2=50cm$

Now using the condition for balanced Wheatstone bridge, we get