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

May 22, 2018

No - as long as the components are ideal.

#### Explanation:

If the capacitor voltage is given by

${V}_{c} = {V}_{0} \sin \left(\omega t + \phi\right)$

then the charge on a capacitor plate is

$q = C {V}_{c} = {V}_{0} C \sin \left(\omega t + \phi\right)$

and the current is

$i = \frac{d}{\mathrm{dt}} q = \omega C {V}_{0} \cos \left(\omega t + \phi\right)$

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

${V}_{R} = i R = \omega C R {V}_{0} \cos \left(\omega t + \phi\right)$
$q \quad = \omega C R {V}_{0} \sin \left(\omega t + \phi + \textcolor{red}{\frac{\pi}{2}}\right)$

Thus ${V}_{R}$ leads ${V}_{C}$ by $\frac{\pi}{2}$ - a result independent of the component values.