Question

The current in a 70.0-mH inductor changes with time as i = 4.00t² ? 8.00t, where i is in amperes and t is in seconds.

(a) Find the magnitude of the induced emf at t = 1.00 s.
in mV

(b) Find the magnitude of the induced emf at t = 4.00 s.
in mV

(c) At what time is the emf zero?
in s

Answer 1

Emf is given by

a) I = 4.00t² ? 8.00t

dI/dt = 8.00t - 8.00

at t= 1.00 sec

dI/dt = 0

therefore,

emf = -L*0 = 0

b) at t= 4.00 seconds,

dI/dt = (8.00)*(4.00)-8.00 = 32.00

therefore,

emf = -L(32) = -(70 x 10^-3)(32) = - 2240 mV

c) for emf to be zero

-L(dI/dt)=0

or dI/dt=0

implies that (8.00)*t - 8.00 = 0

i.e, t=1 s