Question

In the given circuit a metre bridge is shown in the balanced state. The metre bridge wire has a resistance of $1\Omega$ ${cm}^{-1}$. calculate the unknown resistance $X$ and the current drawn from the is the battery of a negligible internal resistance if the magnitude of y is $6\Omega$ . If at the balancing point. we interchange the position of the galvanometer and the cell, how it will affect the position of the galvanometer.

Answer 1

At balanced state
$\frac{X}{Y}=\frac{40}{60}=\frac{2}{3}\Rightarrow X=\frac{2}{3}Y-\frac{2}{3}?6$
$\therefore X=4\Omega$
$4\Omega$ and $6\Omega$ are in series, the equivalent resistance is given by
$R_{rq}=4\Omega +6\Omega =10\Omega$
$4\Omega$ and $6\Omega$ are in series $R_{eq}=10\Omega$
Resistance of bridge wire=1 ohm/cm x 100cm=$100\Omega$
$10\Omega$ and $100\Omega$ are in parallel$=1000/110\Omega =0.09\Omega$ Current $=\frac{6}{9.09}$
There will be no change in the balancing length if we interchange position of galvanometer and cell.