Question

In the circuit shown in figure the reading of ammeter is the same with both switches open as with both closed. The resistance $R$ is $100\times X$in ohms. (ammeter is ideal)The value of $X$ is:

Answer 1

When both switches are opened:- $I_1\Rightarrow \frac{1.5}{450}$

When both switches are closed:- $I_2\Rightarrow \frac{1.5}{300+\frac{100R}{100+R}}$

Now Current I in ammeter $\Rightarrow \left(\frac{R}{R+100}\times \frac{1.5}{300+\frac{100R}{100+R}}\right)=\frac{1.5}{450}$

$450R=(R+100)(300+\frac{100R}{100+R})$

$450R=30000+300R+100R$

$450R=30000+400R$

$50R=30000$

$R=\frac{3000}{5}=600\Omega$