# Question about omega (angular velocity)

1. Nov 25, 2008

### ThomasHW

For a capacitor in an AC circuit, does $$\omega$$ = $$\frac{1}{RC}$$ always?

I have voltages such as Vg = 2cos(105t) V. When finding the capacitance using the formula C = $$\frac{1}{jwc}$$ would I use $$\omega$$ = 105 or would I use $$\omega$$ = $$\frac{1}{RC}$$?

2. Nov 25, 2008

### saltine

RC is the time constant of an RC circuit.

Last edited: Nov 25, 2008
3. Nov 25, 2008

### ThomasHW

Does it change anything if the circuit involves an op-amp?

4. Nov 25, 2008

### saltine

When people say "RC" circuit they usually mean that there is no op-amp. Some op-amp circuits with resistor and capacitor still have the time constance RC.

The impedance of a capacitor is still 1/jωC in either case.

Last edited: Nov 25, 2008
5. Nov 25, 2008

### ThomasHW

If I had a voltage Vg = 2cos(105t) V going into the op-amp, would I still use 105 rad/s as my angular velocity, or $$\frac{1}{RC}$$?

6. Nov 25, 2008

### saltine

Your question doesn't make a lot of sense to me, but ω is 105.

I said something wrong previous, the time constant is RC.

Sometimes when you are working with a system, the equation ωc = 1/RC would come up. This ωc is the cutoff frequency. Are you getting ω and ωc mixed up? ωc is a property of the circuit. ω is a parameter of the input.

7. Nov 25, 2008

### ThomasHW

Probably. I've had to use RC for a high-pass and low-pass filter, but I guess that's because of they have a cut-off frequency.

I guess I'm confused as to when RC and when to use 1/jwc.

8. Nov 25, 2008

### saltine

ωc is a property of a circuit. Suppose you were to sketch the Bode plot of an RC low pass filter. For the magnitude plot, if you just draw the linear approximation, you get two lines segments that meet at a frequency. The frequency that they meet is ωc. Because ωc is where the curve bends, ωc is also called the corner frequency. The significant of ωc is that it is where the input sinusoid gets 'cutoff'.

ω is the frequency of the input. In this low pass example, if ω > ωc, then the input is cutoff.

Zc(jω) = 1/jωC is the impedance of a capacitor. It is the ratio of the voltage and current across a capacitor. It is the ratio Vc(jω)/Ic(jω). It is analogous to resistance, where R = V/I.