Solving LCR Circuit: Find C, I_rms, I_rms at Resonance

[tomrja]

Homework Statement

Consider a series LCR circuit with R= 69.0 Ω and L= 0.100 H, driven by a sinusoidal emf with E_rms= 6.70 V at frequency f= 250 Hz. The sinusoidal current leads the emf by 54.0 degrees.

a) Calculate the capacitance C.
b) What is the rms current in the circuit?
c) If the frequency of the emf is changed to the resonant frequency of the circuit, what is the rms current?

Homework Equations

tan(phi)=(WL-(1/WC))/R

I_p= V^p/Z = V_p/sqrt(R^2+(X_L-X_C)^2)

I_rms=I_P/sqrt(2)

W=2*pi*f

W_o=1/sqrt(LC) resonant frequency

The Attempt at a Solution

I solved tan(phi)=(WL-(1/WC))/R for C and got C=1/(W(WL-Rtan(phi)) then plugged in all given info to solve for C. It says that the answer is wrong and I am assuming that I plugged in the wrong phi. "The sinusoidal current leads the emf by 54.0 degrees." I don't know what this means. I have not started on the other two parts of the problem because I need to find C first. What am I doing wrong? Thanks!

 

[cupid.callin]

Hi tomrja
(have a phi: φ)

tan(phi)=(WL-(1/WC))/R

i didn't read all of your post but the thing i quoted is wrong

$$tan\phi = \frac{\frac{1}{wC} - wL}{R}$$

thats because current in capacitor leads voltage by 90 and lags in inductor by 90

 

[cupid.callin]

and for i_RMS use

i_RMS = E_RMS/Z

 

[tiny-tim]

hi tomrja!

"The sinusoidal current leads the emf by 54.0 degrees." I don't know what this means.

it means that if V = V_maxsinωt, then I = I_maxsin(ωt + 54°)

in other words, the impedance is Z = |Z|e^i54π/180