RC Series Circuit

In an RC series circuit, the resistor and the capacitor are connected in series configuration, which means that the current flowing through the circuit passes through both components one after the other. The resistor resists the current flow, while the capacitor stores energy in the form of an electric field. Lets explore the RL series circuit in the following example.

Phasor Notation

Refer to [Fig. 1]. where

Impedance diagram:

See [Fig. 3].

Voltage:

Ohms laws:

Kirchhoff's voltage law:

as applied.

Phasor diagram:

Note that for the phasor diagram of [Fig. 4], I is in phase with the voltage across the resistor and leads the voltage across the capacitor by $90^\circ$.

Time domain:

In the time domain, A plot of all of the voltages and the current of the circuit appears in [Fig. 5]. Note again that $i$ and $v_R$ are in phase and that $v_C$ lags $i$ by $90^\circ$.

Power:

The total power in watts delivered to the circuit is where E and I are effective values and $\theta_T$ is the phase angle between E and I, or where I is the effective value, or, finally

Power factor:

The power factor $F_p$ of the circuit is $\cos 53.13^\circ =0.6$ leading, where $53.13^\circ$ is the phase angle between E and I.
If we write the basic power equation $P = EI \cos \theta$ as follows: where E and I are the input quantities and P is the power delivered to the network, and then perform the following substitutions from the basic series ac circuit: we find Further supporting the fact that the impedance angle $\theta$ is also the phase angle between the input voltage and current for a series ac circuit. To determine the power factor, it is necessary only to form the ratio of the total resistance to the magnitude of the input impedance. For the case at hand, as found above.