Question

A 12.0 V dc battery having no appreciable internal resistance, a 153.5 Ω resistor, an 11.4 mHinductor, and an open switch are all connected in series.

Part A

After the switch is closed, what is the time constant for this circuit ?

Part B

After the switch is closed, what is the maximum current that flows through it ?

Part C

What is the current 72.7 μs after the switch is closed ?

Part D

After the switch is closed, what is the maximum energy stored in the inductor?

Answer 1

a)
time constant,
tau = L/R
= 11.4*10^-3 / (153.5)
=7.43*10^-5 s
Answer: 7.43*10^-5 s

b)
maximum current,
Io = V/R
=12/153.5
= 0.078 A
Answer: 0.078 A

c)
for LR circuit:
I(t) = Io * (1 - e^-t/tau)
= 0.078 * (1-e^((-72.7*10^-6) / 7.43*10^-5))
= 0.078 * (1-e^(-0.9785)
= 0.049 A
Answer: 0.049 A

d)
Emax = 0.5*L*Io^2
=0.5*(11.4*10^-3)*(0.078)^2
= 3.47*10^-5 J
Answer: 3.47*10^-5 J