Question

Resistances are connected in a meter bridge circuit as shown in the figure. The balancing length l1 is 40 cm. Now an unknown resistance x is connected in series with P and new balancing length is found to be 80 cm measured from the same end. Then the value of x will be ________ Ω.

Answer 1

$\frac {P}{40}=\frac {Q}{60}$ ⋯(1)

$\frac {P+x}{80}=\frac {Q}{20}$ ⋯(2)

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

$\frac {4}{4+x}×2=\frac 13$
$24 = 4 + x$
$x = 20$

So, the amswer is $20$.