 # Series RLC Circuits

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

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

[more] ,

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.

[less]

Contributed by: S. M. Blinder (February 2008)
Open content licensed under CC BY-NC-SA

## Snapshots   ## Details

Snapshot 1: effect of induction dominates; and voltage leads current (ELI)

Snapshot 2: effect of capacitance dominates; and current leads voltage (ICE)

Snapshot 3: circuit fulfills resonance condition; and current and voltage are in phase

 Feedback (field required) Email (field required) Name Occupation Organization Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback. Send