- RL series circuit
- RC series circuit
- RLC series circuit

## RL Series Circuit

In an RL series circuit, a pure resistance (R) is connected in series with a coil having the pure inductance (L). To draw the phasor diagram of RL series circuit, the current *I* (RMS value) is taken as reference vector because it is common to both elements.

Voltage drop V_{R} is in phase with current vector, whereas, the voltage drop in inductive reactance V_{L} leads the current vector by 90^{o} since current lags behind the voltage by 90^{o} in the purely inductive circuit. The vector sum of these two voltage drops is equal to the applied voltage V (RMS value).

The power waveform for RL series circuit is shown in the figure. In this figure, voltage wave is considered as a reference. The points for the power waveform are obtained from the product of the corresponding instantaneous values of voltage and current.

It is clear from the power waveform that power is negative between 0 and φ and between 180^{o} and (180^{o} + φ). The power is positive during rest of the cycle.

Since the area under the positive loops is greater than that under the negative loops, the net power over a complete cycle is positive. Hence a definite quantity of power is consumed by the RL series circuit. But power is consumed in resistance only; inductance does not consume any power.

## RC Series Circuit

In an RC series circuit, a pure resistance (R) is connected in series with a pure capacitor (C). To draw the phasor diagram of RC series circuit, the current *I* (RMS value) is taken as reference vector. Voltage drop V_{R} is in phase with current vector, whereas, the voltage drop in capacitive reactance V_{C} lags behind the current vector by 90^{o}, since current leads the voltage by 90^{o} in the pure capacitive circuit. The vector sum of these two voltage drops is equal to the applied voltage V (RMS value).

The power waveform for RC series circuit is shown in the figure. In this figure, voltage wave is considered as a reference. The points for the power waveform are obtained from the product of the corresponding instantaneous values of voltage and current. It is clear from the power waveform that power is negative between (180^{o} – φ) and 180^{o} and between (360^{o} – φ) and 360^{o}. The power is positive during rest of the cycle.

Since the area under the positive loops is greater than that under the negative loops, the net power over a complete cycle is positive. Hence a definite quantity of power is consumed by the RC series circuit. But power is consumed in resistance only; capacitor does not consume any power.

## RLC Series Circuit

In an RLC series circuit a pure resistance (R), pure inductance (L) and a pure capacitor (C) are connected in series. To draw the phasor diagram of RLC series circuit, the current *I* (RMS value) is taken as the reference vector. The voltages across three components are represented in the phasor diagram by three phasors V_{R}, V_{L} and V_{C} respectively.

The voltage drop V_{L} is in phase opposition to V_{C}. It shows that the circuit can either be effectively inductive or capacitive. In the figure, phasor diagram is drawn for the inductive circuit. There can be three cases of RLC series circuit.

- When X
_{L}> X_{C}, the phase angle φ is positive. In this case, RLC series circuit behaves as an RL series circuit. The circuit current lags behind the applied voltage and power factor is lagging. In this case,

if the applied voltage is represented by the equation;

v =*V*_{m}sin ωt

then, the circuit current will be represented by the equation;

i =*I*_{m}sin (ωt – φ). - When X
_{L}< X_{C}, the phase angle φ is negative. In this case, the RLC series circuit behaves as an RC series circuit. The circuit current leads the applied voltage and power factor is leading. In this case, the circuit current will be represented by the equation:

i = I_{m}sin (ωt + φ). - When X
_{L}= X_{C}, the phase angle φ is zero. In this case, the RLC series circuit behaves like a purely resistive circuit. The circuit current is in phase with the applied voltage and power factor is unity. In this case, the circuit current will be represented by the equation:

i =*I*_{m}sin (ωt).

- AC Fundamentals
- RMS value of AC Current
- Purely Resistive | Inductive | Capacitive Circuit
- RL | RC | RLC Series Circuits
- Power Factor in AC Circuit
- Power Factor Improvement Using Capacitor Bank
- Star Connection
- Delta Connection
- Power Measurement in Three Phase Circuits