Question

In a metre bridge the null point is found at a distance of $40cm$ from A . If a resistance of $12\Omega$ is connected in parallel with ${}^{\prime }{S}^{\prime }$ , the null point occurs at $50cm$ from A . determine value of ${}^{\prime }{R}^{\prime }$ and ${}^{\prime }{S}^{\prime }$

Answer 1

When $12\Omega$ resistance is not connected in parallel to S than we can write,

$R=S\frac{l_1}{100-l_1}$

$l_1=40cm$

$\therefore R=S\left(\frac{40}{60}\right)=\frac{2}{3}S$ __(I)

Now when $12\Omega$ is connected in parallel to S, then

The effective resistance can be written as

$\frac{1}{S_1}=\frac{1}{S}+\frac{1}{12}=\frac{12+5}{12S}\Rightarrow S_1=\frac{12S}{(12+5)}$

Now we can write

$R=S\frac{l^{\prime }}{100-l^{\prime }}\Rightarrow l^{\prime }=50cm$

i.e. $R=\frac{12S}{(12+5)}\times \frac{50}{50}=\frac{12S}{12+5}$ __(II)

Using eq (II) and (I)

$\frac{2}{3}S=\frac{12S}{12+5}\Rightarrow (12+5)2=36$

$\Rightarrow 24+25=36\Rightarrow 25=12\Rightarrow S=6\Omega$

and $R=\frac{2}{3}\times 6=4\Omega$