Question

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


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

• A. $\frac{1}{20}[1-e^{-t}]$
• B. $\frac{1}{40}[1-e^{-t}]$
• C. $\frac{1}{20}{e}^{-t}$
• D. $\frac{1}{10}{e}^{-t}$

Answer 1

The correct option is B $\frac{1}{40}[1-e^{-t}]$

$i=\frac{ϵ}{2R}[1-e^{-\frac{t2R}{2L}}]$
$=\frac{0.5}{20}[1-e^{-t}]$

$i=\frac{1}{40}[1-e^{-t}]$