Phase shift in AC Circuits by Stephen Bucaro

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:

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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