In a metre bridge experiment null point is obtained at $20 \mathrm{~cm}$ from one end of the wire when…
In a metre bridge experiment null point is obtained at $20 \mathrm{~cm}$ from one end of the wire when resistance $X$ is balanced against another resistance $Y$. If $X < Y$, then where will be the new position of the null point from the same end, if one decides to balance a resistance of $4 X$ against Y?
$50 \mathrm{~cm}$
$80 \mathrm{~cm}$
$40 \mathrm{~cm}$
$70 \mathrm{~cm}$
Solution
We have from meter bridge experiment, $\frac{\mathrm{R}_1}{\mathrm{R}_2}=\frac{\ell_1}{\ell_2}$, where $\ell_2=\left(100-\ell_1\right) \mathrm{cm}$ In the first case, $X / Y=20 / 80$ In the second case $\frac{4 X}{Y}=\frac{\ell}{100-\ell}$ $\ell=50 \mathrm{~cm}$.