The current in an RL circuit is zero at time t = 0 and increases to half its final value in 6.0 s.The time constant of this circuit is approximately
A)6.0 s
B)12 s
C)8.7 s
D)3.0 s
E)9.8 s

Question

Quizplus · Accepted Answer

The current in an RL circuit can be described using the equation:

I = I0(1 - e^(-t/τ))

where I0 is the final value of the current, τ is the time constant, and t is the time.

We are told that the current in this circuit is zero at t=0 and increases to half its final value in 6.0 s.

Plugging in these values, we get:

0.5I0 = I0(1 - e^(-6/τ))

Simplifying this equation, we can cancel out the I0 terms and solve for τ:

0.5 = 1 - e^(-6/τ)
0.5 = e^(-6/τ)
ln(0.5) = -6/τ
τ = -6/ln(0.5) ≈ 8.7 s

Therefore, the time constant of this circuit is approximately 8.7 s, which is closest to option C.

The Current in an RL Circuit Is Zero at Time