RLC Series Circuits: Introduction

Consider an RLC series circuit consisting of a resistor, an inductor, and a capacitor connected to an AC voltage source. A current, which varies sinusoidally over time, flows through the circuit, and this can be expressed by the following equation:  

where I₀ is the current amplitude, and Φ is the phase angle between the current and the applied voltage. The phase angle is the amount by which the voltage and current are out of phase with each other in a circuit.

The RLC series circuit can be analyzed using a phasor diagram. The voltage phasor of the resistor points in the same direction as the current phasor and has a phase difference of 0°. In the case of an inductor and capacitor, the voltage phasor leads and lags the current phasor by an angle of 90°. At any instant, the voltage across the RLC is the sum of the components of the individual vectors. The projection of the vector sum of the phasors onto the vertical axis is the sum of the vertical projections of the individual phasors. By adding the phasors vectorially, the projection of the resultant phasor onto the vertical axis can be obtained: