1.5 Power

Formula for power

Before electric power is defined, the formula is given to calculate it. The following formula can be used for any component in electric or electronic circuits:

P = V . I

in which P is the power consumed or generated by the component, V is the voltage across the component, and I is the current through the component. Again, this formula always works. But what does it mean? And how should the result be interpreted? In order to answer these questions, let’s start with a dimensional analysis.

The unit of power

The unit of voltage is volt (V), and since voltage is energy per unit of charge, 1 volt corresponds to 1 joule (J) per coulomb (C). The unit of current is ampere (A), and 1 ampere corresponds to 1 coulomb (C) per second (s). So the unit of power is (the brackets mean “the unit of…”):

[P] = [V].[I] = V . A = J/C . C/s = J / s = W

The unit of power is watt (W). 1 watt corresponds to 1 joule per second. Power indicates how fast energy is consumed (or generated).

Power versus energy

For many students it takes a while before they grasp the concepts of power and energy, and the relation between them. Here is an analogy that might help. The amount of fuel (typically expressed in liters or gallons) in your car corresponds with an equivalent amount of energy (expressed in joule). The more fuel you have, the more energy you have at your disposal. Amount of fuel and amount of energy are linearly related. The amount of fuel and thus the amount of energy also determines how far you can go with your car.

Once you start riding your car, you will consume fuel. The rate at which this happens corresponds to power. Your fuel consumption (typically expressed in liters/100 km or gallons/100 km) is linearly related with power (expressed in joule per second or watt). If you accelerate fast or drive uphill, more power is involved than accelerating slowly or driving downhill.

The relation between power and energy is given in this formula, assuming the power P is constant:

ΔE = P . Δt

in which ΔE is the energy consumption during time interval Δt. So, the longer a certain power consumption is maintained, the more energy is needed. In car language, the farther you want to ride, the more fuel you need. Power can thus be defined as the rate at which energy is consumed (or generated):

P = ΔE / Δt

Power in a resistor

basics_power_resistorFigure1.6 Power in a resistor

Basics - Level 3

A few simple questions to practice.

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