Question

It takes 2.21 ms for the current in an LR circuit to increase from zero to 0.55 its maximum value.

a. Determine the time constant of the circuit.

b. Determine the resistance of the circuit if L = 34.0 mH.

Answer 1

Part A:

We know that current grows exponentially by the formula:

i(t)=ε/R(1-e^-t/τ) where i is a function of t and τ is the time constant. So at time t=2.21 ms the current is .55i_maximum.

.55i_max=ε/R(1-e^-2.21ms/τ) and since i_max=ε/R

.55=1-e^-2.21ms/τ

.45=e^-2.21ms/τ

ln(.45)=-2.21ms/τ

τ=-2.21ms/ln(.45)

τ=2.768ms

Part B:

τ=L/R

R=L/τ

R=34.0mH/2.768ms

R=12.28 Ω