Electric Current, Ohm’s Law, and Electric Circuits

ISAT 241

Fall 2002

David J. Lawrence

Electric Current Consider a bar of material in which positive

charges are moving from left to right:

imaginary surface

I

Electric current is the rate at which charge passes through the surface, Iavg = Q/t, and the instantaneous current is I = dQ/dt.

Electric Current

IdQ

dt

SI unit of charge: Coulomb (C) SI unit of current: Ampere (1A= 1C/s) A current of 1 ampere is equivalent to 1

Coulomb of charge passing through the surface each second.

Electric Current By definition, the direction of the current is in the

direction that positive charges would tend to move if free to do so, i.e., to the right in this example.

In ionic solutions (e.g., salt water) positive charges (Na+ ions) really do move. In metals the moving charges are negative, so their motion is opposite to the conventional current.

In either case, the direction of the current is in the direction of the electric field.

Electric Current Na+ ions moving through salt water

Electrons moving through copper wire

E I

E I

Electric Current The electric current in a conductor is given

by

wheren = number of mobile charged particles (“carriers”) per unit volumeq = charge on each carriervd = “drift speed” (average speed) of each carrierA = cross-sectional area of conductor

In a metal, the carriers have charge q e.

I nqv Ad

Electric Current

The average velocity of electrons moving through a wire is ordinarily very small ~ 10-4 m/s.

It takes over one hour for an electron to travel 1 m!!!

E I

Ohm’s Law For metals, when a voltage (potential

difference) Vba is applied across the ends of a bar, the current through the bar is frequently proportional to the voltage.

area

A

Vb VaE

I

The voltage across the bar is denoted:

Vba = VbVa .

Ohm’s Law

IR

V or V R Iba ba 1

This relationship is called Ohm’s Law.

The quantity R is called the resistance of the conductor.

R has SI units of volts per ampere. One volt per ampere is defined as the Ohm (. 1=1V/A.

Ohm’s Law is not always valid!!

Ohm’s Law The resistance can be expressed as

where

is the length of the bar (m)

A is the cross-sectional area of the bar (m2)

, “Rho”, is a property of the material called the

resistivity. SI units of ohm-meters (-m).

RA

area

A

Vb VaE

I

Ohm’s Law

The inverse of resistivity is called conductivity:

So we can write

1 1

RV

I A A

Resistance and Temperature The resistivity of a conductor varies with

temperature (approximately linearly) as

where resistivity at temperature T (oC)

oresistivity at some reference temperature To (usually 20oC)

“temperature coefficient of resistivity”.

Variation of resistance with T is given by

o oT T1 ( )

R R T To o 1 ( )

Electrical Power

The power transferred to any device carrying current I (amperes) and having a voltage (potential difference) V (volts) across it is

P = VI Recall that power is the rate at which energy

is transferred or the rate at which work is done.

Units: W (Watt) = J/s

Electrical Power

Since a resistor obeys Ohm’s Law

V = IR , we can express the power dissipated in a resistor in several alternative ways:

P VI I RV

R 2

2