# How to Calculate the Phase Angles in RLC Circuits

John Foxx/Stockbyte/Getty Images

An RLC circuit contains a resistor, an inductor and a capacitor. RLC circuits are a type of alternating current circuit, where the magnitudes of the voltage and current follow the pattern of a sine wave.

Phase angle indicates the difference between the voltage and current waves -- voltage and current have the same wave pattern across a resistor, but the voltage wave is 90 degrees ahead of the current wave for an inductor and 90 degrees behind for a capacitor. When an inductor and capacitor combine, as in an RLC circuit, the phase angle is somewhere between -90 degrees and 90 degrees. To calculate phase angle, you must know resistance, inductance and capacitance, as well as frequency or angular frequency.

- An RLC circuit contains a resistor, an inductor and a capacitor.
- When an inductor and capacitor combine, as in an RLC circuit, the phase angle is somewhere between -90 degrees and 90 degrees.

Calculate angular frequency if you know the frequency. Multiply frequency by 2_pi = 6.28 to get angular frequency. If the frequency is 50 Hz, for example, 6.28_50 Hz = 314 Hz.

Multiply the angular frequency by the inductance to get the inductive reactance. If inductance is 0.50 henries, for example, (314 Hz)*(0.50 H) = 157 ohms.

Divide 1 by the angular frequency times the capacitance to get the capacitive reactance. If capacitance is 10 microfarads, for example, 1/(314 Hz)*(0.000001F) = 318.5 ohms.

Compare the inductive and capacitive reactances. If they're equal, the phase angle is 0 degrees.

Subtract the capacitive reactance from the inductive reactance if they are not equal. For example, 157 ohms - 318.5 ohms = -161.5 ohms.

Divide the result by the resistance. If the resistance is 300 ohms, for example, -161.5 ohms/300 ohms = -0.538.

Take the inverse tangent of the result to get the phase angle. For example, tan^-1(-0.538) = -28.3 degrees.

References

- Georgia State University; Phase; R. Nave
- "College Physics, Volume 10"; Raymond Serway, et al.; 2008
- Ohio State University; R-L-C Circuits and Resonant Circuits; K. K. Gan; 2004

Resources

Writer Bio

Petra Wakefield is a writing professional whose work appears on various websites, focusing primarily on topics about science, fitness and outdoor activities. She holds a Master of Science in agricultural engineering from Texas A&M University.