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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# RL Circuit

**Physics Forums | Science Articles, Homework Help, Discussion**