32.6:
RLC Series Circuits: Introduction
In an RLC series circuit, the resistor, the inductor, and the capacitor are connected in a series combination across an AC voltage source, and have resistance and reactances.
The current and the voltage of the AC source vary sinusoidally over time, where they are out of phase with each other by a phase angle Φ.
The voltage is either mostly in phase with the current for a resistive circuit, or leads the current for an inductive circuit, or lags the current for a capacitive circuit.
According to Kirchhoff's loop rule, the instantaneous voltages across the resistor, the inductor, and the capacitor add to give the instantaneous source voltage.
The current phasor can be represented by a phasor diagram. Similarly, the three voltage phasors are vectorially added to arrive at the source voltage phasor.
The phasor diagram leads to the amplitude and the phase angle of the source voltage phasor. When the phase angle is positive, the circuit is more inductive, whereas if it is negative, the circuit is more capacitive.
32.6:
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:
Suggested Reading
- OpenStax. (2019). University Physics Vol. 2. [Web version]. Retrieved from https://openstax.org/books/university-physics-volume-2@8ede2ba/pages/15-3-rlc-series-circuits-with-ac