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Inductive Reactance Formula Help (page 2)

By — McGraw-Hill Professional
Updated on Oct 3, 2011

Rl Phase Angle

When the resistance in an electronic circuit is significant compared with the inductive reactance, the alternating current resulting from an alternating voltage lags that voltage by less than 90° (Fig. 9-9). If the resistance R is small compared with the inductive reactance X L , the current lag is almost 90°; as R gets relatively larger, the lag decreases. When R is many times greater than X L , the phase angle, ø RL , is nearly zero. If the inductive reactance vanishes altogether, leaving a pure resistance, then the current and voltage are in phase with each other.

The value of the phase angle ø RL , which represents the extent to which the current lags the voltage, can be found using a calculator that has inverse trigonometric functions. The angle is the arctangent of the ratio of inductive reactance to resistance:

Waves and Phase Inductive Reactance Rl Phase Angle

Fig. 9–9. An example of current that lags voltage by less than 90°, as in a circuit containing resistance and inductive reactance.

ø RL = arctan( X L /R )

Inductive Reactance Practice Problems

Practice 1

Find the phase angle between the AC voltage and current in an electrical circuit that has 50 ohms of resistance and 70 ohms of inductive reactance. Express your answer to the nearest whole degree.

Solution 1

Use the above formula to find ø RL , setting X L = 70 and R = 50:

Waves and Phase Inductive Reactance Rl Phase Angle

Practice problems for these concepts can be found at:  Waves and Phase Practice Test

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