 # Phasor Diagram for Series RLC Circuits

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This Demonstration shows a phasor diagram in an AC series RLC circuit. The circuit consists of a resistor with resistance , an inductor with inductance , and a capacitor with capacitance . The current in an RLC series circuit is determined by the differential equation

[more] ,

where and is the AC emf driving the circuit. The angular frequency is related to the frequency in hertz (Hz) by . In this Demonstration, the amplitude is set to 10 volts (V). You can vary the frequency in Hz, the resistance in ohms ( ), the inductance in millihenries (mH), and the capacitance in microfarads ( F). , , , , .

The phase of is the same as that of . leads  . The phase of lags that of by .

The voltage and current are out of phase by an angle , where .

When  the effect of inductance is dominant; then , and the RLC circuit's total voltage leads the current . When the capacitance contribution is dominant, , and the current leads the voltage. When the circuit has a pure resistance or when the resonance condition or is satisfied, then , meaning that the voltage and current are in phase.

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Contributed by: Anping Zeng (July 2011)
(Sichuan Chemical Technical College)
Open content licensed under CC BY-NC-SA

## Snapshots   ## Details

Snapshot 1: , , leads the current Snapshot 2: , , leads the current Snapshot 3: or , , resonance