In an AC circuit with a capacitor or an inductor there is a phase shift between voltage and current. In this article you learn how to calculate the amount of that phase shift.

In a purely resistive AC circuit, current and voltage are in phase.

In a purely capacitive AC circuit, current leads voltage by 90 degrees. There is a +90 degree phase shift.

In a purely inductive AC circuit, current lags voltage by 90 degrees. There is a -90 degree phase shift.

**Series Resistor Capacitor Circuit**

In an AC RC circuit (resistive/capacitive) circuit, current leads voltage by less than 90 degrees. In a circuit with 5 ohm resistor and a 100 uF capacitor, there will be a 79.3 degree phase shift.

**How to Calculate Phase Shift in a Series RC Circuit**

To calculate the phase in a series RC circuit, use R (resistance) as one
side, and Xc (capacitive reactance) as the other side of a right triangle,
and use the trigonometry arctangent function (symbol tan^{-1}) to
calculate the phase angle.

Note: the ^{-1} does not mean tangent raised to the power of -1).

Let's use the values from the example above.

5 ohm resistor

.0001 farad capacitor

60 Hz frequency

10 volts

You'll need Xc in the formula, and the formula for Xc is:

1/2nfc.So, Xc = 1/ (2 * pi * 60 * 0.0001) = 26.525 ohms

Then to calculate the phase angle:

Phase_angle = tan^{-1} Xc/R = 79.3 degrees

<script> var r = 5; var c = .0001; var f = 60; var XC = 1/(2 * Math.PI * f * c); // Math.atan() function returns the // arctangent (in radians) var inrads = Math.atan(XC/5); // phase in degrees alert(inrads * (180/Math.PI)); </script>

Shown above is a short script to calculate phase shift in an RC circuit.

**Series Resistor Inductor Circuit**

In an AC RL circuit (resistive/ inductive) circuit, current lags voltage by less than 90 degrees. In a circuit with 5 ? of resistance and a 10 mH inductor, there will be a 37.0 degree phase shift.

**How to Calculate Phase Shift in a Series RL Circuit**

Let's use the values from the example above.

5 ohm resistor

.01 henry inductor

60 Hz frequency

10 volts

You'll need XL in the forula, and the formula for XL is:

So, Xl = 2 * pi * 60 * 0.01 = 26.525 ohms

Then to calculate the phase angle:

Phase_angle = tan^{-1} Xl/R = 37.0 degrees

<script> // Xc is 2nfc var XC = 2 * Math.PI * 60 * .01; // Math.atan() function returns the // arctangent (in radians) var inrads = Math.atan(XC/5); // phase in degrees alert(inrads * (180/Math.PI)); </script>

Shown above is a short script to calculate phase shift in an RL circuit.

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