Electrical Power

Power questions are one step past Ohm's law and use the same three quantities. The only new thing is the formula, and it has three forms because Ohm's law lets you substitute.

The three formulas

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Start with P = V x I. That is the definition: power is voltage times current, measured in watts.

Now substitute Ohm's law:

You do not have to memorize three formulas. Memorize P = VI and Ohm's law, and substitute whichever quantity you are missing. But recognizing the other two forms is faster in the exam room, so both are worth having.

Worked examples

A device draws 3 amperes at 120 volts. What power does it consume?

3 times 120 is 360 watts.

A 5-ohm resistor carries 2 amperes. How much power does it dissipate?

I squared R: 2 squared is 4, times 5 is 20 watts.

A 12-volt supply is across a 6-ohm resistor. What power is dissipated?

V squared over R: 144 divided by 6 is 24 watts.

Check that last one the long way: current is 12 over 6, which is 2 amperes, and power is 12 times 2, which is 24. Agreed.

Power against energy

Power is the rate of energy use. Energy is power multiplied by time.

A 100-watt bulb left on for 10 hours uses 1,000 watt-hours, which is 1 kilowatt-hour.

An electricity bill charges for kilowatt-hours, which is energy, not power. A question asking what the utility bills for wants energy.

A 1,500-watt heater run for 2 hours uses 3 kilowatt-hours. That is the calculation: watts times hours, divided by 1,000 to get kilowatt-hours.

The squared term matters

P = I squared x R means power rises with the square of the current.

Double the current and the heat quadruples. Triple it and the heat is nine times greater.

That is why:

• Overloaded wiring gets hot fast. A modest increase in current is a large increase in heating.
• Transmission lines run at high voltage. For a given power, higher voltage means lower current, and lower current means much less energy lost as heat in the line. That is the real reason the grid steps voltage up for transmission, and it is a question.

Power in series and parallel

Total power is the sum of the power in each component, in either arrangement. Power always adds, which is the one quantity that behaves the same way in both.

In series, the same current flows through everything, so by P = I squared R the largest resistance dissipates the most power.

In parallel, every branch has the same voltage, so by P = V squared / R the smallest resistance dissipates the most power.

Those two point in opposite directions, which is the question. In series, big resistance means more heat; in parallel, small resistance means more heat, because the small one draws the most current.

Practical ratings

Appliances are rated in watts, and dividing by the supply voltage gives the current they draw.

A 1,200-watt appliance on a 120-volt supply draws what current?

1,200 divided by 120 is 10 amperes.

That calculation decides whether a circuit is overloaded, which is why it appears in questions about breakers and wiring.

Horsepower is a power unit too, and one horsepower is about 746 watts, which comes up with motors.

What you can skip

Across all 1,358 Electronics Information questions in our bank:

• Power factor in power calculations. The power lesson uses resistive loads; power factor is taught in the AC and DC lesson, and its only calculation is the one shown there.
• Three-phase power formulas never appear as calculations.
• Efficiency calculations are rare (5 mentions). Know that output is always less than input, with the difference lost as heat.
• Horsepower conversions come up three times. 746 watts per horsepower is enough.

Where people lose points

Confusing power with energy. Watts are a rate; kilowatt-hours are a quantity.

Forgetting to square the current in P = I squared R.

Using the wrong form of the formula for the quantities given. Pick the form that uses what you have.

Saying the largest resistor always dissipates the most power. Only in series.

Forgetting to divide by 1,000 when converting watt-hours to kilowatt-hours.

Work one in under a minute

A 60-watt bulb and a 100-watt bulb are both designed for 120 volts. Which has the higher resistance?

Rearrange P = V squared / R to R = V squared / P.

Same voltage on top, so the higher power means the lower resistance.

The 60-watt bulb has the higher resistance: 14,400 over 60 is 240 ohms, against 14,400 over 100, which is 144 ohms.

The intuition that a brighter bulb must have more resistance is backward, and this is the question that catches it.

Where this leads

Power ratings decide wire sizes and fuse ratings, and the heating effect is the reason circuit protection exists.