A coil with a self-inductance of 6.0 H is connected to a dc source through a switch. As soon as the switch is closed at t = 0 s, the rate of change of current is 2.0 A/s. What is the emf induced in this coil at t = 0 s?
A) 6.0 V
B) 3.0 V
C) 12 V
D) 1/3 V
E) 0 V

Question

Quizplus · Accepted Answer

We know that the emf induced in a coil is given by:
emf = -L*(dI/dt)

At t=0s, the rate of change of current is given as 2.0 A/s. Therefore, the emf induced in the coil is:
emf = -6.0 H * (2.0 A/s) = -12 V

Since the emf induced is negative, the direction of induced current will be opposite to the direction of the applied current. Therefore, the net emf across the coil will be:
emf_net = V_applied + emf_induced

At t=0s, the switch is closed and hence the applied voltage is zero. Therefore,
emf_net = -12 V

Since we are interested in the magnitude of the emf (not its sign), we get:
|emf_net| = |emf_induced| = 12 V

Therefore, the correct answer is option C) 12 V.

A Coil with a Self-Inductance of 6