# Finding Irms in a circuit

1. Mar 24, 2010

### ndoc

1. The problem statement, all variables and given/known data
The figure below shows a load resistor that has a resistance of RL = 20.6 Ω connected to a high-pass filter consisting of an inductor that has inductance L = 3.20-mH and a resistor that has resistance R = 4.00-Ω. The output of the ideal ac generator is given by = (100 V) cos(2πft).
Image at: http://www.webassign.net/tipler6/29-p-041.gif
(note: image inserted by mentor)

Find the rms currents in all three branches of the circuit if the driving frequency is 475 Hz.
For Irms, I(Rl)rms, I(L)rms

Find the fraction of the total average power supplied by the ac generator that is delivered to the load resistor if the frequency is 475 Hz.

Find the fraction of the total average power supplied by the ac generator that is delivered to the load resistor if the frequency is 1840 Hz.

2. Relevant equations
z= sqrt(R^2 +(wL-1/wC)2)
I=Vsource/Ztotal
I = Imax*cos(2*pi*f*t-theta)

3. The attempt at a solution

So I am in a low level physics and we got stuck with a problem that my TA has told me he hasn't had to solve until about his senior year. He doesn't really understand why we have this problem. This is way over my head and I will need a lot of help if anyone is willing to give it. If anyone would like to help (which I would highly appreciate) please talk to me like I'm dumb because I am VERY confused. Thanks.

Combining the inductor and load resistor we get a z equation of z=R+ (Rl(wL)^2/(Rl^2+(wL)^2)) + Rl^2*w*L/(Rl^2+(wL)^2)i where i means an imaginary number

Then |Z|total= sqrt([Zreal]^2+[Zimaginary]^2)

Then I = Vsource/Ztotal where Vsource=Vrms=100/sqrt(2)
Then I = Imax*cos(2*pi*f*t - theta)

I attempted and got |Z|= 8.47 and I = 8.35A which I thought would be Irms but I was wrong