In Fig. there is a frame consisting of two square loops having resistors and inductors as shown. This frame is placed in a uniform but time-varying magnetic field in such a way that one of the loops is placed in crossed magentic field and the other is placed in dot magnetic field. Both magnetic fields are perpendicular to the planes of the loops.
If the magnetic field is given by `B = (20 + 10 t) Wb m^(-2)` in both regions `[l = 20 cm, b = 10 cm`, and `R = 10 Omega`, `L = 10 H`),

The current in the frame as a funtion of time will be

Options

A. `(1)/(20) (1 - e^(-t))`
B. `(1)/(40) (1 - e^(-t))`
C. `(1)/(20) e^(-t)`
D. `(1)/(10) e^(-t)`

Answer

B

Explanation

Since the field is increasing in inside direction in bigger loop, so the current will be induced to oppose this increasing flux. Hence in anticlockwise direction.
`phi = BA = B(l^(2) + b^(2))`
`|epsilon| = |(dphi)/(dt)| = (dB)/(dt) (l^(2) + b^(2)) = 0.5 V`
`i = (epsilon)/(2R)[1 - e^(-(t2R)/(2L))] = (0.5)/(20) [1 - e^(t)]`

`i = (1)/(40)[1 - e^(-t)]`