Question

Resistances 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

$\frac{P}{40}=\frac{Q}{60}\dots \left(1\right)$

$\frac{P+x}{80}=\frac{Q}{20}\dots \left(2\right)$

$\frac{P}{P+x}\times \frac{80}{40}=\frac{20}{60}$

$\frac{4}{4+x}\times 2=\frac{1}{3}$

$24=4+x$

$x=20$