Electricity and Magnetism

Current and Resistance

Electric current

Electric current is a concept describing the flow of charges. Specifically, it is defined as the amount of charge passing through a cross section per unit time:

I = DQ/Dt

By convention, the direction of a current refers to the direction of the flow of positive charges. If charge carriers carry negative charges, such as the electrons in a metal wire, the direction of the current is opposite to the direction of motion of charge carriers.

The SI unit of electric current is ampere (A):

1 A = 1 C/s

Electric current can be written in terms of microscopic quantities as

I = nqvdA


Example 17.2 The drift speed in a copper wire

Resistance and Ohm's law

For many materials, it is found that the current is proportional to the applied voltage, which is called the Ohm's law. Mathematically, it is expressed as

I = (1/R)V


V = RI


R = V/I

is called the resistance. Resistance has a unit of V/A which is called ohm (W).

1 W = 1 V/A


Resistance depends on the dimension of an object. The related concept that depends only on the material is the resistivity r which is related to the resistance R by

R = r(l/A)

where l is the length and A is the area.

The resistivity r is a characteristic of a material that describes how good a conductor it is. Good conductors have small resistivities. Insulators have large resistivities.

The SI unit of resistivity is Wm.

Example 17.4 The resistance of nichrome wire

Electric energy and power

P = (DQ V)/Dt


P = IV

For a resistor, the power can also be written as

P = I2R = V2/R

Charges lose potential energy as they move across a resistor. This energy is transformed into other forms of energy such as heat and light (electromagnetic radiation).

When applied to a battery, the equation P=IV gives the power that is being generated by the battery, i.e., the rate at which electric energy is being generated from other forms of energy such as chemical energy.

It should be clear how energy is conserved.

Example 17.6 The power consumed by an electric heater

Example 17.7 Electric rating of a lightbulb

Example 17.8 The cost of operating a lightbulb

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Copyright 1997 by Bo Gao. All rights reserved.