Question

In the circuit shown, when keys $K_{1}$ and $K_{2}$ both are closed, the ammeter reads $I_{0}$. But when $K_{1}$ is open and $K_{2}$ is closed the ammeter reads $I_{0} / 2$. Assuming that ammeter resistance is much less than $R_{2}$, the values of $r$ and $R_{1}$ are

• A. $25 \,\Omega, 50\, \Omega$
• B. $25\, \Omega, 100\, \Omega$
• C. $0,100\, \Omega$
• D. $0,50\, \Omega$

Answer 1

Answer: (D)

When $K_{1}$ and $K_{2}$ both are closed $R_{1}$ is short circuited and circuit resistance will be
$R_{ eq }=(50+r)\, \Omega$
When $K_{1}$ is open and $K_{2}$ is closed, current remains half.
Therefore net resistance of the circuit becomes two times.
$50+r+R_{1}=2(50+r)$
For the given options in questions, above equation is satisfied for
$r=0 $ and $R_{1}=50\, \Omega$