The reading of an ammeter in the circuit

(i) `I` when key `K_(1)` closed key `K_(2)` is open
(ii) `I//2` when both keys `K_(1) and K_(2)` are closed Find the expression for the resistance of `X` in terms of the resistances of R and S

Options

A. `100,50`
B. `50,100`
C. `0,100`
D. `0,50`

Answer

d

Explanation

When `K_(1)` is closed the resistance `R_(1)` is ineffective
`:. I_(0) = (E )/(100 + r) = (E )/(2(50 + r)) or r = 0 `
When `R_(1)` is open, then
`(I_(0))/(2) = (E )/(2(R_(1) +50)) = (E )/(2 xx 100) or R_(1) = 50 Omega`