Answer to Question 6

An inductor of inductance 0.47 mH has a resistance of 4.0 W and is connected to a DC supply of 20 V.

a. What is the steady state current?

b. What is the time constant?

c. What is transient time?

d. What is the value of the instantaneous reverse voltage after 0.1ms?

e. What is the value of the instantaneous current after 0.1 ms?

a. I = V/R = 20 V ÷ 4.0 W = 5.0 A

b. t = L/R = 0.47 × 10^{-3} H ÷ 4.0 W = 1.175 × 10^{-4} s = 0.12 ms

c. Transient time = 5 t = 5.88 × 10^{-4} s = 0.59 ms

d. Formula:

V = 20 V × e ^ (- 1.0 × 10^{-4} s ÷ 1.175 × 10^{-4} s) = 20 V × e ^ - 0.851 = 20 V × 0.427 = 8.54 V

(The measured voltage would be 20 V - 8.54 V = 11.5 V)

e. Formula:

I = 4.0 A × (1 - 0.427) = 4.0 A × 0.573 = 2.29 A = 2.3 A (2 s.f.)