In the circuit shown, 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` is Omega are

Options

A. 25,50
B. 25100
C. 0,100
D. 0,50

Answer

D

Explanation

When `K_1` and `K_2` both are closed `R_1` is short circuited,
`R_("net")=(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.
or `(50+r)+R_1=2(50+r)`
of the given options the above equation is satisfied if
`r=0` and `R_1 =50 Omega`