Question

In a series RC circuit, does the phase difference between the capacitor and the resistor voltages depend on the values of R and C?

Answer 1

No - as long as the components are ideal.

Explanation:

If the capacitor voltage is given by

`V_c = V_0 sin(omega t+phi)`

then the charge on a capacitor plate is

`q = CV_c = V_0 C sin(omega t + phi)`

and the current is

`i= d/dt q = omega C V_0 cos (omega t+phi)`

Since the components are in series, the same current flows through the resistor. Hence the voltage drop across the resistor is

`V_R = iR = omega CR V_0 cos (omega t +phi)`
`qquad = omegaCRV_0 sin(omega t + phi + color(red)(pi/2))`

Thus `V_R` leads `V_C` by `pi/2` - a result independent of the component values.