In a series RC circuit, 12 V(rms) is measured across the resistor and 15 V(rms) is measured across the capacitor. What is the rms source voltage?
In ac circuits, Kirchoff's Voltage Law still applies (sum of volt rises equals sum of volt drops around closed loop), but the important thing to realize is that we apply the phasor sum of the voltages, where magnitude and phase angle is important. That is, we view the voltages as complex numbers and write them in polar form.(You may think of it as a vector sum where magnitude and direction is critical, and hence Pythagoras is valid for right angled triangles for example).
According to the theory, a resistor has no phase shift, capacitor has -90 degree (leading) phase angle, inductor has +90 degree (lagging) phase angle. Phasors rotate anticlockwise as usual.
The full details are in the sketch :