Question

The current in a 90.0 mH inductor changes with time as
= 1.00
− 6.00
, where
is in

amperes and

is in seconds. Solve for the magnitude of the induced emf at (a)
= 1.00

and
= 4.00
. (c) At what time is the emf zero?

Answer 1

Given:

• Current in a inductor :
• Inductor value :

The relation between induced emf, inductor and current is given by,

Magnitude of emf is then,

Plugging the value of current in above equation and differentiating current with respect to time we get,

(a) at time t = 1.00 second :

This is the magnitude of the induced emf in volt at time t=1 s.

(b) at time t = 4.00 second :

This is the magnitude of the induced emf in volt at time t =4s

​​​​​​(c) Time when emf is zero :

We have,

If emf if zero, i.e. , then

Thus, the emf is zero at time t=3 second.

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