I want to check my answers for this problem: Part c) below doesn't agree with the book. And even though part a) agrees, I'm not sure about my method.(adsbygoogle = window.adsbygoogle || []).push({});

I've attached a figure for reference.

For the attached figure, the switch is closed fo t<0, and steady-state conditions are established. The switch is thrown open at t = 0.

a) Find the initial voltage across L just after t = 0. Which end of the coil is at higher potential: A or B?

c) How long after t = 0 does the current in the 6kOhm resistor have the value 2.00 mA.

For part a), I used Kirchhoff's loop rule to get the currents at steady state.

6kOhmI1 = 18V

I1 = 3mA

2kOhmI2 - 0.4H(di2/dt) = 18V ==> di2/dt = 0 at steady state.

I2 = 9ma

Itotal = 12mA

Once the switch is thrown open I have an RL series circuit.

In a series circuit I should be the same across both resistors so:

I1 goes to zero, so I total in the circuit is 9mA.

6kOhmI + 2kOhmI - 0.4H(di/dt) = 0

0.4(di/dt) = 8kOhmI = 8kOhm(9mA) = 72Volts; B has the higher potential.

If my reasoning above is correct then for part c)

I = Iinitial(e^(-t/T)) where T = L/R = .4/8000 = 50 microseconds

2mA = 9mA(e^(-t/50us)

ln(1/6) = -t/50us

t = 50ln(1/6) = 75.2 microseconds. The answer is the book is 75.2us

Thanks in advance for the help.

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# Homework Help: RL Circuit

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