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

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Answer 1 · 2018-05-22T10:18:11

No - as long as the components are ideal.

If the capacitor voltage is given by

$V_{c} = V_{0} sin (ω t + ϕ)$ $V_c = V_0 sin(omega t+phi)$

then the charge on a capacitor plate is

$q = C V_{c} = V_{0} C sin (ω t + ϕ)$ $q = CV_c = V_0 C sin(omega t + phi)$

and the current is

$i = \frac{d}{d t} q = ω C V_{0} cos (ω t + ϕ)$ $i= d/dt q = omega C V_0 cos (omega t+phi)$

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

$V_{R} = i R = ω C R V_{0} cos (ω t + ϕ)$ $V_R = iR = omega CR V_0 cos (omega t +phi)$
$qquad = omegaCRV_0 sin(omega t + phi + color(red)(pi/2))$

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