Question about omega (angular velocity)

[ThomasHW]

For a capacitor in an AC circuit, does [tex]\omega[/tex] = [tex]\frac{1}{RC}[/tex] always?

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

 

[saltine]

ω=10⁵ rad/s

RC is the time constant of an RC circuit.

 

[ThomasHW]

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

 

[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.

 

[ThomasHW]

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

 

[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 ω_c = 1/RC would come up. This ω_c is the cutoff frequency. Are you getting ω and ω_c mixed up? ω_c is a property of the circuit. ω is a parameter of the input.

 

[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.

 

[saltine]

ω_c 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 ω_c. Because ω_c is where the curve bends, ω_c is also called the corner frequency. The significant of ω_c is that it is where the input sinusoid gets 'cutoff'.

ω is the frequency of the input. In this low pass example, if ω > ω_c, then the input is cutoff.Z_c(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 V_c(jω)/I_c(jω). It is analogous to resistance, where R = V/I.