Frequency at which current precedes voltage

[jackloring]

Homework Statement

So, I wish I could draw this for you all, but here goes:

We are given a resistor at 8 ohms in series with a capacitor at 30µF. The task is to determine the frequency at which the current precedes the voltage by 30°.

Just in case you're wondering, we are given the answer which is f=1149 Hz, but I can't figure out how to achieve that.

Homework Equations

f=1/T, T=2pi/$$\omega$$, $$\Delta$$$$\theta$$/2pi = $$\Delta$$t/T

The Attempt at a Solution

It seems to me like we aren't given enough information. What I've tried so far is:

T= (30°/360°)*$$\Delta$$t

How am I supposed to figure that out with two unknown variables? I also can't calculate $$\omega$$ since I don't know the frequency to begin with. Any ideas? Thanks for the help.

 

[berkeman]

Homework Statement

So, I wish I could draw this for you all, but here goes:

We are given a resistor at 8 ohms in series with a capacitor at 30µF. The task is to determine the frequency at which the current precedes the voltage by 30°.

Just in case you're wondering, we are given the answer which is f=1149 Hz, but I can't figure out how to achieve that.

Homework Equations

f=1/T, T=2pi/$$\omega$$, $$\Delta$$$$\theta$$/2pi = $$\Delta$$t/T

The Attempt at a Solution

It seems to me like we aren't given enough information. What I've tried so far is:

T= (30°/360°)*$$\Delta$$t

How am I supposed to figure that out with two unknown variables? I also can't calculate $$\omega$$ since I don't know the frequency to begin with. Any ideas? Thanks for the help.

One way to do it is to write the KCL equation at the output node (the node between the resistor and cap), and solve for the frequency where you get that phase shift.

What is the equation that relates the current through a capacitor to the voltage across the capacitor? Use that equation and show us the KCL for the transfer function from Vi to Vo ...

 

[jackloring]

I am not quite sure, but I think the equation that you mentioned is:

i(t)= (Vo/R)*e^(-t/$$\tau$$o)

But, I see no node between the resistor and capacitor.

 

[jackloring]

But, if there were a node there as you mentioned, I suppose KCL would be:

Ir - Ic = 0

 

[berkeman]

But, if there were a node there as you mentioned, I suppose KCL would be:

Ir - Ic = 0

Yes, any junction between components can be called a node.

And yes, that is the basic equation for the KCL, with Ir = Ic.

But for the equation relating the current through and voltage across a capacitor, I want you to write the differential equation relating them. One quantity is related to the time derivative of the other... Then solve for the transfer function Vo/Vi, and plug in a sinusoidal source for Vi(t).

 

[vk6kro]

With a series circuit like this, you can draw an impedance diagram:

[PLAIN]http://dl.dropbox.com/u/4222062/Z%20diagram.PNG

From this you can work out the value of the capacitor's reactance, Xc.

Then, you know the size of the capacitor, so at what frequency does it have this reactance?

 

[jackloring]

Thanks for the nice diagram vk6kro, I understand how to calculate Xc and Z, however, when I have these values, what do you mean by size of the capacitor? Is that somehow different than its value of 30µF? And furthermore, what would the formula look like for the frequency at which this reactance Xc occurs? Would it be different than:

f = 1/T?

Because if it's the same, then I feel like am stuck back at the beginning.

 

[vk6kro]

The size of the capacitor is 30 uF.

Tan (30) = Xc / 8

The reactance of a capacitor Xc is 1 / (2 * pi * F * C) where C is in Farads.

So, you just need to solve for F.