Question

Resistance are connected in a meter bridge circuit as shown in the figure. The balancing length $l_1$ is $40cm$. Now an unknown resistance $x$ is connected in series with $P$ and new balancing length is found to be $80cm$ measured from the same end. Then the value of $x$ will be _____ $\Omega$

Answer 1

Answer: 20

Initially, $\frac{P}{Q}=\frac{40cm}{60cm}=\frac{2}{3}....$(1)
Finally, $\frac{P+x}{Q}=\frac{80cm}{20cm}=\frac{4}{1}.....$(2)
Divide (2) by (1)
$\frac{P+x}{P}=4\times \frac{3}{2}=6$
$\Rightarrow 1+\frac{x}{P}=6\Rightarrow \frac{x}{P}=5$
$\therefore x=5P=5\times 4=20\Omega$