chacm Problem 21.49 12 a Problem 21.4 Part A A 1.70 mH inductor is connected in

Question

chacm Problem 21.49 12 a Problem 21.4 Part A A 1.70 mH inductor is connected in series with a de battery of negligible iternal resistance, a 0840 k resistor, and an open switch. How long afer the switch is closed will i take for the current in the cirouit to reach half of its maximum value? Submit Incorrect: Try Again: 3 attempts remaining Part B How long aner re swich is closed w take for ne energy stored n the inductor to reach harofits manmun vahw? Hints My Answers Give Up Incorrect: Try Again: 5 attempts remaining Provide Eeedback Continu MacBook Pro

Explanation / Answer

L = 1.7*10^-3 H
R = 840

This will produce a very short time constant T = L / R = 2.02*10^-6 s

The current is

i = Imax * (1 - e^(-t/T))

When i = 0.5*Imax
0.5 = 1 - e^(-t/T)
e^(-t/T) = 1 - 0.5 = 0.5
-t / T = ln(0.5) = -0.69315
t = 0.69315 *2.02*10^-6 s = 1.4*10^-6 s = 1.4 s


Emax = 0.5*L*Imax^2

When E = 0.5*Emax
i^2 / Imax^2 = 0.5
so i = Imax / sqrt(2) = 0.7071*Imax

0.7071 = 1 - e^(-t/T)
e^(-t/T) = 1 - 0.7071 = 0.2929
-t / T = ln(0.2929) = -1.228
t = 1.228 * 2.02*10^-6 s = 2.48*10^-6 s = 2.48 s

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