Q. 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} in Ω are

(a) 25, 50

(b) 25, 100

(c) 0, 100

(d) 0, 50

Ans: (d)

Solution : when keys K_{1} and K_{2} both are closed , resistance R_{1} is ineffective .

Net resistance R’ = 50 + r

$ \displaystyle I_0 = \frac{E}{50+r}$ …(i)

when keys K_{1} is open

Net resistance R” = R_{1} + 50 + r

$ \displaystyle \frac{I_0}{2} = \frac{E}{R_1 + 50 + r}$ …(ii)

On dividing (i) by (ii)

$ \displaystyle 2 = \frac{R_1 + 50 + r}{50 + r}$

100 + 2 r = R_{1} + 50 + r

50 + r = R_{1}

r = 0 , R_{1} = 50