Question

In the given circuit, ammeter reading is same when both switches S${}_1$, S${}_2$ are closed or opened. The value of resistance $R$ is

• A. $200\Omega$
• B. $100\Omega$
• C. $400\Omega$
• D. $600\Omega$

Answer 1

Answer: (D)

$600\Omega$

When both are opened reading of (A)

is $\frac{1.5}{450}=\frac{1}{300}A$

When both are closed reading of (A)

is $I=\left[\frac{1.5}{300+\frac{100R}{100+R}}\right]\times \frac{R}{R+100}$

$\Rightarrow \frac{1}{300}=\frac{1.5R}{(R+100)\left[\frac{30000+400R}{100+R}\right]}$

$450R=30000+400R$

$\Rightarrow 50R=30000$

$R=\frac{30000}{50}$

$R=600\Omega$