An RLC 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
,
where
and
is the AC emf driving the circuit. The angular frequency ω 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 (
). The voltage V in volts and current
in milliamperes (mA) are shown in the plot over a 50-millisecond (msec) window.
The sinusoidal curves for voltage and current are out of phase by an angle
, where
.
When the effect of inductance is dominant, then
, and the voltage
leads the current. When the capacitance contribution is dominant (for small values of
), then
, and the current leads the voltage. The mnemonic "ELI the ICEman" summarizes these relationships. When the circuit has a pure resistance or when the resonance condition
is satisfied, then
, meaning that the voltage and current are in phase.
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