# Electricity and Magnetism

### Current and Resistance

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 = nqv_{d}A

where

- n is the number density of the charge carrier, i.e.
number of carriers per unit volume.
- q is the charge of each carrier.
- A is the area of the cross section.
- v
_{d} is the *drift velocity*.

Example 17.2 The drift speed in a copper wire

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

or

V = RI

where

R = V/I

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

1 W = 1 V/A

Resistivity

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 W·m.

Example 17.4 The resistance of nichrome wire

P = (DQ V)/Dt

thus

P = IV

For a resistor, the power can also be written as

P = I^{2}R = V^{2}/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.
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