A coil having n turns and resistance `R Omega` is connected with a galvanometer of resistance `4R Omega`. This combination is moved in time t seconds from a magnetic field `W_(1)` weber to `W_(2)` weber. The induced current in the circuit is

Options

A. `-(n(W_(2)-W_(1)))/(5Rt)`
B. `-(n(W_(2)-W_(1)))/(Rt)`
C. `-((W_(2)-W_(1)))/(5Rnt)`
D. `-((W_(2)-W_(1)))/(Rnt)`

Answer

A

Explanation

Induced e.m.f. `e= -(nd phi)/(dt)`
`:.` Induced current `I = (-(ndphi)/(dt))/(R')` where `R'=4R+R=5R Omega`
In this problem, W is used for `phi - flux`
`:. I = n/(R')(dW)/(dt) but dW=W_(2)-W_(1)` and `dt = t, R'=5R`
`:. I = -(n(W_(2)-W_(1))/(5Rt))`.