Starting from zero, the electric current takes 2 seconds to reach half its maximum possible value in an RL circuit with a resistance R, an inductance L and a battery of emf E. How long will the current take to reach 75% its maximum value (measured from the moment when I = 0)?
A)8 s
B)4 s
C)10 s
D)1 s
E)2 s

Question

Quizplus · Accepted Answer

The time constant τ for an RL circuit is L/R. The current I(t) in an RL circuit is given by I(t) = I_max(1 - e^(-t/τ)). Given that it takes 2 seconds to reach half its maximum value, we can use this to find τ. Solving 0.5 = 1 - e^(-2/τ) gives τ = 2/ln(2). To find the time to reach 75% of the maximum value, solve 0.75 = 1 - e^(-t/τ), which gives t = 4 seconds.

Starting from Zero, the Electric Current Takes 2 Seconds to Reach