What is the Frequency for In-Phase Current and Voltage in RLC Circuit?

[monnapomona]

Homework Statement

This was a part question and I got everything else but one part (#4!):

1) A 60-Hz generator with an RMS potential of 240 V is connected in series with a 3350 Ohm resistor and a 1.5 microFarad capacitor. What is the RMS current in the circuit?
I_RMS = 6.34 * 10^-2 A

2) In the previous question, what is the phase angle between the current and total voltage (in degrees)?
$\phi$ = 27.8 deg

3) What would be the average (RMS) power consumed in the circuit in the previous question?
P_avg = 13.5 W

4) At what frequency would the circuit in the previous problems have to be operated in order to have the current and total circuit voltage be in phase?

Homework Equations

z = sqrt(R^2 + X_C^2) <-- not sure if I had to use this one
X_C = 1/ωC
ω = 2πf

The Attempt at a Solution

I don't really know how to solve this (or if I'm even using the right equations to solve for it) but I tried solving for f in the formula and I got 72.3 as the answer and it was wrong in the homework assignment. I think phase difference is pi/2 so if it's in phase, do I need to add pi/2 to my final answer...? I'm very lost with this question as you can tell.

 

[rude man]

Homework Statement

This was a part question and I got everything else but one part (#4!):

1) A 60-Hz generator with an RMS potential of 240 V is connected in series with a 3350 Ohm resistor and a 1.5 microFarad capacitor. What is the RMS current in the circuit?
I_RMS = 6.34 * 10^-2 A

2) In the previous question, what is the phase angle between the current and total voltage (in degrees)?
$\phi$ = 27.8 deg

3) What would be the average (RMS) power consumed in the circuit in the previous question?
P_avg = 13.5 W

4) At what frequency would the circuit in the previous problems have to be operated in order to have the current and total circuit voltage be in phase?

Homework Equations

z = sqrt(R^2 + X_C^2) <-- not sure if I had to use this one
X_C = 1/ωC
ω = 2πf

The Attempt at a Solution

I don't really know how to solve this (or if I'm even using the right equations to solve for it) but I tried solving for f in the formula and I got 72.3 as the answer and it was wrong in the homework assignment. I think phase difference is pi/2 so if it's in phase, do I need to add pi/2 to my final answer...? I'm very lost with this question as you can tell.

Well, for one thing, it's a trick question.

What is the expression for phase angle between total applied voltage and current for a series R-C circuit?

Or: go back to part 2 and change the frequency until you get in-phase between total applied voltage and current.

 

[monnapomona]

Well, for one thing, it's a trick question.

What is the expression for phase angle between total applied voltage and current for a series R-C circuit?

Or: go back to part 2 and change the frequency until you get in-phase between total applied voltage and current.

I think it's cos$\phi$ = R/Z, Z = sqrt(R^2 + X_C^2)... I don't know if I thinking about this correctly but does in phase mean that the angle = 0?

 

[rude man]

I think it's cos$\phi$ = R/Z, Z = sqrt(R^2 + X_C^2)... I don't know if I thinking about this correctly but does in phase mean that the angle = 0?

That formula is correct.
Yes, "in phase" means zero phase angle between V and i.

So now what does X_C have to be to make the phase angle zero?

 

[monnapomona]

That formula is correct.
Yes, "in phase" means zero phase angle between V and i.

So now what does X_C have to be to make the phase angle zero?

Hmm... well if cos^-1(1) = 0, then my answer has to equal 1 somehow... so wouldn't X_C need to be 0 because:

cos$\phi$ = 3500 $\Omega$ / sqrt((3500 $\Omega$)^2 + 0^2) = 1
$\phi$ = cos^-1(1) = 0 deg

 

[mojo11jojo]

Hi physics 126 classmate here. I'm also stuck on this question. I propose to get I and V in phase, the frequency has to be infinity.

 

[monnapomona]

Hi physics 126 classmate here. I'm also stuck on this question. I propose to get I and V in phase, the frequency has to be infinity.

Yeah, that's what I was thinking cause if the X_C is 0 then we would have to be dividing over 0 to get f since X_C = 1/(2πf*C)... is that what you did?

 

[mojo11jojo]

yup just yolo'd and typed infinity into the answer slot. It is correct :) Also the last question, the answer is The current will be the same at very low frequencies and at very high frequencies only.

 

[monnapomona]

yup just yolo'd and typed infinity into the answer slot. It is correct :) Also the last question, the answer is The current will be the same at very low frequencies and at very high frequencies only.

Say what! Haha awesome.

Ah, I got that one! Thanks! :P

 

[mojo11jojo]

Enjoy the free 100% for anyone googling answers

 

[rude man]

Say what! Haha awesome.

Ah, I got that one! Thanks! :P

Told yu it was a trick question!

But - what's this about the current being the same at very low & very high frequencies?

 

[mojo11jojo]

It's a separate question altogether not included in the original post