Conceptual Physics

Below we derive the first equation, P = IǻV. Before deriving it, we review why a

resistor consumes power. The essential component of many household devices í

toasters, light bulbs, electric burners í is a resistor.

As electrons move through any resistor, they collide with the atoms that make up the

resistor. The electrons lose energy in these collisions and the atoms gain it, which

increases the temperature of the resistor. More current through a given resistor means

more collisions, and a warmer resistor. This analysis confirms one aspect of the power

equation: Power increases with the amount of current.

To derive the power equation, we will consider the work done on the electron by the

electric field. We will state the work in terms of the potential difference: It equals the

charge times the potential difference. We will use that equation to derive the power

equation.

Variables

Strategy

1. State the equation that relates work, charge and potential difference.


2. Divide by the time interval ǻtto calculate the work per unit time, which is power.

Equations

Here, work is related to charge and potential difference by

W = ǻPE = qǻV

We will also use the definitions of power and current.

Step-by-step derivation

We state the relationship between work and potential difference, then divide by the time

interval ǻt. This converts work to power and total charge to current, resulting in the first

formulation of the power equation.

Ohm’s law is used to derive the other equations for power in the second line of Equation

1. For instance, ǻV= IR, so we can substitute for ǻV and conclude that P= I^2 R. The
   equation P= IǻV holds true for all electrical devices, while the other equations apply
   solely to power (energy) dissipated as heat by resistors.

Electric power

Function of current, potential difference

P = IǻV

P = I^2 R = ǻV^2 /R

P = power

I = current

ǻV = potential difference

R = resistance

How much power is being

supplied to this hot plate?

P = IǻV

P = (8.00 A) (120 V)

P = 960 W

work W

total charge moving across resistor q

potential difference across resistor ǻV

time interval ǻt

power consumed by resistor P

current passing through resistor I

Step Reason

1. W = qǻV work and potential difference

2. divide by ǻt

3. P = IǻV definitions of power and current

(^464) Copyright 2000-2007 Kinetic Books Co. Chapter 25