Question

A 12.0-V battery is connected into a series circuit containing a 13.0-Ω resistor and a 3.00-H inductor. (a) In what time interval will the current reach 50.0% of its final value? (b) In what time interval will the current reach 90.0% of its final value?

Answer 1

E = battery Voltage = 12 volts

R = resistance = 13 ohm

L = inductor = 3 H

T = time constant = L/R = 3/13 = 0.231 sec

a)

current is given as

I = I_o (1 - e^-t/T)

0.5 I_o = I_o (1 - e^-t/0.231)

t = 0.16 sec

b)

current is given as

I = I_o (1 - e^-t/T)

0.9 I_o = I_o (1 - e^-t/0.231)

t = 0.532 sec