Alternating Current Power Calculations

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  • 0:04 AC Circuits
  • 1:25 Power Equations
  • 2:29 Calculation Example
  • 3:54 Lesson Summary
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Lesson Transcript
Instructor: David Wood

David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.

After watching this lesson, you will be able to explain the difference between AC and DC circuits and calculate AC current, AC voltage and AC power using both rms values and peak values. A short quiz will follow.

AC Circuits

When you study physics, you spend most of the time studying direct current (or DC). It's simpler, makes it easier to understand the basic concepts, and it's better for visualization. But take a look around you. Look at the wall sockets nearby and the light bulbs above your head. Both of these things, and indeed most things around you, are powered by alternating current (or AC). The band AC-DC might have been partial to both, but nearly everything you experience in life will be AC-powered.

Alternating current is where current switches direction super-fast instead of flowing just one way around a circuit - one way then the opposite way, over and over. The most common rate at which this happens is 60 Hz, or 60 switches per second. This creates a current that varies sinusoidally, which means that it varies in the form of a sine curve, like this one:

Sine Curve of AC Circuit
sine curve of AC current

Since the current is switching, so is the voltage. It also follows a sine curve. Because of this, we tend to express current and voltage as special averages called rms (or root mean squared). An AC circuit will have an rms current and an rms voltage. And those values are defined by the following equations:

RMS Equations
rms equations

You can see that V-zero is the peak or maximum voltage, and I-zero is the peak or maximum current. Those are the tops and bottoms of the sine curve.

Power Equations

But this lesson is titled 'AC Power,' so how do we calculate the power used by an AC circuit? As discussed in another video lesson, power is the energy used per second, measured in watts (or Joules per second). And in a circuit, you can calculate it by multiplying the current by the voltage. We can do exactly the same thing for an AC circuit; we just use the rms current and rms voltages. So below is our basic equation for power in an AC circuit: the rms voltage, measured in volts, multiplied by the rms current, measured in amps.

Basic Power Equation
power equation

But what if you don't know the rms voltage or rms current? What if, instead, you know the peak voltage V-zero and peak current I-zero? Well, then we would need to use the previous equations for rms voltage and rms current. But to avoid using more than one equation, we can substitute these equations into the power equation, like this:

Power Equation
simplified power equation

This then simplifies to tell us that the power used in an AC circuit is equal to the peak current, multiplied by the peak voltage, divided by two.

Calculation Example

Okay, let's try an example! You're doing some tests on an energy-saving light bulb. You find that the maximum voltage it ever uses is 240 volts, and the maximum current that flows through it is 0.12 amps. For a regular light bulb, you look up some values and find that the rms voltage is 120 volts, and the rms current is 0.5 amps. What is the difference in power used by the two light bulbs?

Okay, so we need to figure out how much power is used by each light bulb and then compare them. For the first, we're given maximum values, and for the second, we're given rms values. So, we need to use a different equation for each and then compare the two power values.

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