Question

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.

Answer 1

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

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

Step-by-step 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