# How to Calculate the Phase Angles in RLC Circuits

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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.

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.

- 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.

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.

- Multiply the angular frequency by the inductance to get the inductive reactance.
- If capacitance is 10 microfarads, for example, 1/(314 Hz)*(0.000001F) = 318.5 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

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