# Serial RC Circuit

A serial RC circuit contains a resistor and a capacitor connected in serial.

The alternating voltage U is applied to the circuit, so the alternating current is flowing through the branch:

The resistor's voltage:

The capacitor's voltage lags behind the current by phase angle π/2:

where X_{C} = 1/ω·C - capacitive resistance.

The vector diagram for all voltages (voltage triangle):

After we divide all voltages by current I, we get the resistance triangle:

where R - the active resistance, X_{C} - the capacitive resistance, Z - the total resistance (or impedance). The total resistance is:

The total voltage lags behind current by phase angle φ:

The angle goes in clockwise direction (from current vector to voltage vector), hence it is negative here.

The power coefficient is defined as an active and reactive resistance ratio:

The effective current I, flowing through the circuit:

The active power:

The reactive power:

The total power: