In the circuit shown,R = 1200 $\varOmega$,L = 6.0 H,and V = 9.0 V.After switch S is closed,how long will it take the current in the inductor to reach 4.0 mA?
A)2.3 ms
B)2.7 ms
C)3.8 ms
D)5.0 ms
E)7.7 ms

Question

In the circuit shown,R = 1200 $\varOmega$,L = 6.0 H,and V = 9.0 V.After switch S is closed,how long will it take the current in the inductor to reach 4.0 mA? 
A)2.3 ms 
B)2.7 ms 
C)3.8 ms 
D)5.0 ms 
E)7.7 ms

Quizplus · Accepted Answer

We can use the formula for current in an RL circuit:
I (t) = (V/R) [1 - e^(-Rt/L)]

We are given R, L, and V, and need to find the time (t) when the current reaches 4.0 mA (0.004 A). We can rearrange the formula to solve for t:

t = -L/R * ln(1 - I/I₀)

Plugging in our values, we get:

t = -6.0 H / 1200 Ω * ln(1 - 0.004 A / (9.0 V / 1200 Ω))
t ≈ 3.8 ms

So the answer is C.

In the Circuit Shown,R = 1200 Ω\varOmegaΩ ,L = 60 H,and V = 9

In the Circuit Shown,R = 1200 $\varOmega$ ,L = 60 H,and V = 9