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. `(phi_(2) - phi_(1))/(5 R nt)`
B. `(- n(phi_(2) - phi_(1)))/(5 R nt)`
C. `(- (phi_(2) - phi_(1)))/(R nt)`
D. `(- n(phi_(2) - phi_(1)))/(5 Rt)`

Answer

B

Explanation

For n turns
`e = - (n d phi)/(dt) = (n (phi_(2) - phi_(1)))/(t)`
total resistance of the circuit `= R + 4 R = 5 R`
total current in the circuit `I = (e)/(5 R)`
`I = (n (phi_(2) - phi_(1)))/(5 Rt)`