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# Capacitive Reactance Help (page 2)

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By McGraw-Hill Professional
Updated on Aug 30, 2011

## RC Phase Angle

When the resistance R in an electrical circuit is significant compared with the absolute value (or negative) of the capacitive reactance, the alternating voltage resulting from an alternating current lags that current by less than 90°. More often, it is said that the current leads the voltage (Fig. 9-11). If R is small compared with the absolute value of X C , the extent to which the current leads the voltage is almost 90°; as R gets relatively larger, the phase difference decreases. When R is many times greater than the absolute value of X C , the phase angle, ø RC , is nearly zero. If the capacitive reactance vanishes altogether, leaving just a pure resistance, then the current and voltage are in phase with each other.

The value of the phase angle ø RC , which represents the extent to which the current leads the voltage, can be found using a calculator. The angle is the arctangent of the ratio of the absolute value of the capacitive reactance to the resistance:

ø RC = arctan(|X C |/R )

Fig. 9-11. An example of current that leads voltage by less than 90°, as in a circuit containing resistance and capacitive reactance.

Because capacitive reactance X C is always negative or zero, we can also say this:

ø RC = arctan(– X C / R )

## Capacitive Reactance Practice Problems

#### Practice 1

Find the extent to which the current leads the voltage in an AC electronic circuit that has 96.5 ohms of resistance and -21.1 ohms of capacitive reactance. Express your answer in radians to three significant figures.

#### Solution 1

Use the above formula to find ø RC , setting X C = -21.1 and R = 96.5:

ø RC = arctan(| – 21.1|/96.5)

= arctan (21.1/96.5)

= arctan (0.21865)

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

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