A) The current that goes through a 100 mH inductor is given as

i (t) = 6 - 2e^-2t A t > = 0

Find the voltage v (t) across the inductor.

b) The voltage v (t) = 5sin (5t) V is applied across the terminals of a 200 mH inductor. The initial current through the inductor is i (0) = - 10 A. Find the current i (t) through the inductor for t > 0.

A) V (t) = 0.4e^-2t

B) i (t) = (25tsin5t+10) A for t>0

Explanation:

Formula for calculating voltage across an inductor is expressed as:

V = Ldi/dt

Given L = 100mH = 100*10^-3

If i (t) = 6 - 2e^-2t A t > = 0

di/dt = (-2) (-2) e^-2t

di/dt = 4e^-2t

If t ≥ 0

V (t) = 100*10^-3 * (4e^-2t)

V (t) = 0.1*4e^-2t

V (t) = 0.4e^-2t for t≥0

B) Applying the same formula as above

V = Ldi/dt

Vdt = Ldi

V/L dt = di

On integration

Vt/L = i + C

When t = 0, i = - 10A

Substituting the values into the formula

V (0) / L = - 10 + C

0 = - 10+C

C = 10

To get the current i (t) through the inductor for t>0,

Since Vt/L = i + C

Given V (t) = 5sin5t Volts

L = 200mH = 200*10^-3H

C = 10

On substituting

(5sin5t) t/0.2 = i + 10

25tsin5t = i + 10

i (t) = (25tsin5t-10) A for t>0