Find the Driving frequency and phase angle for this R-C phasor problem

[MedEx]

Homework Statement

An alternating emf source with a variable frequency fd is connected in series with a 40.0 Ω resistor and a 29.0 μF capacitor. The emf amplitude is 11.9 V. Consider a phasor diagram for phasor VR (the potential across the resistor) and phasor VC (the potential across the capacitor). (a) At what driving frequency fd do the two phasors have the same length? At that driving frequency, what are (b) the phase angle in degrees, (c) the angular speed at which the phasors rotate, and (d) the current amplitude?

Relevant Equations

ℰ=ℰm*sin(ωdt) ; XC=1/(ωd*C) ; Z=sqrt(R^2+(XL-XC)^2)
i=I*sin(ωdt- ϕ) ; VL= I*XL ; tanϕ= (XL-XC)/R
VR= I*R ; XL=ωd*L
VC=I*XC ; I=ℰ/Z

Using the givens I found ωd=862 rad/s, and with some help I got tanϕ=-1 and Z=56.5685 ohms.
But I can't figure out any of the other variables. I'm not even exactly sure what "driving frequency" is and I can't find an equation for it.

 

[NascentOxygen]

The driving frequency is the frequency of the source signal.
862 radians/sec looks right

 

[MedEx]

The driving frequency is the frequency of the source signal.

Do you know what the equation I would need for that is?

 

[Master1022]

Do you know what the equation I would need for that is?

$\omega = 2 \pi f$ should help you convert from rad/s to Hz. I hope that helps.

 

[MedEx]

$\omega = 2 \pi f$ should help you convert from rad/s to Hz. I hope that helps.

It does! Thanks. so now i found the frequency and the angular frequency. any word on the phase angle or current amplitude?

 

[Master1022]

It does! Thanks. so now i found the frequency and the angular frequency. any word on the phase angle or current amplitude?

For the phase angle, I am assuming that means the phase angle between the $V_r$ and $V_c$ phasors. In that case, you know that the currents are the same through both components (as they are in series), then you know how to get the phasor voltages for both components (via $V = I Z$ as you wrote above). I would advise that you let current act as the reference phasor- by this I mean the one that we measure everything relative to, so we put it on the positive real axis on our phasor diagram. So for example, we know the impedance of a resistor is R (i.e. it is a real number), thus meaning that voltage will just be a scalar multiple of current that is parallel. What can be said for the capacitor? Also, you might think about whether the answer depends on the driving frequency? (BTW, I have just realized that you have calculated tan(phi), so I am guessing that you have this answer already??)

For the amplitude of the current: can you work out the total impedance? If so, can you use $V = I Z$ to solve for I?

Hope that is of some use. I was trying to give hints that wouldn't completely spoil the problem for you.