Question

The output of an AC generator varies sinusoidally, and has a peak amplitude of 18.6 V and a frequency of 140 Hz. It is connected to a 75 H inductor. What is the maximum value of the current?

When the current is a maximum, what is the emf of the generator?

When emf of the generator is -6.51 V and increasing in magnitude what is the current?

Answer 1

Em = 18.6 V, f = 140 Hz, w = 2pi*f = 880 rad/s, L = 75 H

Applied voltage: E = 18.6*sin(880t)
Let I be the current through the inductor, then E = L*(dI/dt)
18.6*sin(880t) = (75)dI/dt
Thus I = (18.6/75)(-1/880)cos(880t) = -0.28*cos(880t) mA

a) maximum value of current is 0.28 mA
b) current and voltage are 90 degrees out of phase, hence voltage is zero when current is max
c) -6.51 = 18.6*sin(880t), when 880t = -0.114*pi.

At that time the current is -0.28*cos(-0.114*pi) = -0.262 mA