AC/Phasor Circuit Output Voltage Question
For a shared current into a resistor and capacitor you might be tempted to say: -
\$V_{SUPPLY} = V_R + V_C\$ (incorrect)
This would not be true because the voltage across a capacitor does not rise and fall sinusoidally as the current rises and falls sinusoidally. For a capacitor the current and voltage looks like this: -

(source: electronics-tutorials.ws)
In other words it is 90 degrees out of phase with voltage. This is because the basic formula for a capacitor is
\$I = C\dfrac{dV}{dt}\$
And, if V is a sinewave voltage then I has to be a cosine current.
If instead of real waveforms we drew them as phasors we would represent the voltages and current like so: -

So now if we want to &quot;relate&quot; Vsupply to the individual voltages of the capacitor and resistor we have to add them using pythagorous i.e.
\$V_{SUPPLY} = \sqrt{V_R^2 + V_C^2}\$.
It follows from this that impedances also add this way.