In the circuit shown, when keys K1 and K2 both are closed, the ammeter reads I0. But when K1 is open and K2 is…..

Q. In the circuit shown, when keys K₁ and K₂ both are closed, the ammeter reads I₀. But when K₁ is open and K₂ is closed the ammeter reads I₀/2. Assuming that ammeter resistance is much less than R₂, the values of r and R₁ in Ω  are

(a) 25, 50

(b) 25, 100

(c) 0, 100

(d) 0, 50

Ans: (d)

Solution : when keys K₁ and K₂ both are closed , resistance R₁ is ineffective .

Net resistance R’ = 50 + r

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

when keys K₁ is open

Net resistance R” = R₁ + 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 = R₁ + 50 + r

50 + r = R₁

r = 0 , R₁ = 50