Lecture 5Current and Resistance

Chapter 17

Outline

• Electric Current• Ohm’s Law• Resistivity• Electrical Energy and Power

Electric CurrentAn electric current is a flow of like charges (positive or negative).The current is the rate at which charge flows through a conducting surface.The direction of an electric current is the direction of positive charge flow (current carriers are electrons).

QI t

Unit of current is ampere (A)1A 1C/s

1A of current is equivalent to 1C of charge passing through the crossectional area in a time interval of 1 second.

Electric Current

Microscopic view of electric current

Representation of electric current

ResistanceWhen a potential difference (V) is applied across the end of a conductor, the current in the conductor is proportional to the applied voltage.

I ~ V

The proportionality constant R is called the resistance.It remains constant over a wide range of currents and voltages.

VR I

Ohm’s Law

The relationship between the current and voltage is called Ohm’s Law after George Ohm.

V is the potential drop across the resistorI is the current in the resistor

Materials with a constant resistance are called ohmic, those with variable resistance are nonohmic.

V = IR Unit of resistance is ohm ()

Using Ohm’s Law

Problem: How long can a car with a 12V battery of 60 A h capacity have the lights, of total resistance of 4 , on before the battery runs down?

Solution: I = V /R = 12V / 4 = 3 ATime t = 60 A h / 3 A = 20 hours

ResistivityElectrons, driven by the electric force inside a conductor, collide with atoms and experience an internal friction.This is the origin of a material’s resistance.The resistance of an ohmic conductor is directly proportional to its length (l) and inversely proportional to its cross-sectional area (A).

lR = A

The constant is called the resistivity of the material.=R A / l is measured in m (ohm-meters).

Resistance of a WireProblem: Calculate the resistance per unit length of an aluminum (Al) wire of radius 0.5 mm.

Solution: The cross-sectional area is A = r2

A = 3.1416 (0.5 103 m)2 = 7.85 107 m2

The resistivity of Al is 2.82 10 8 mResistance per unit length is R/l = /A

2.82 10 8 m = = 0.036 /mA 7.85 107 m2

Electrical Energy and Power

The chemical energy of a battery is constantly transformed into internal energy of a conductor.

Q V = I V t

Power P = I V V = I R P=I2R= (V)2/R

Unit of power1W = 1V 1A

Units of Power and Energy

Unit of power is Watt (W).Power is energy per unit time.Thus, energy can be measured in kilowatt-hours.This is not a standard unit, because the SI unit for power is W and for time is s.

1 kWh = (103 W) (3600 s) = 3.6 106 J

Summary

• Electric current is a flow of charge in an electric field

• Resistance of a conductor is the ratio of the potential difference across the conductor to the current

• Ohm’s law states that the potential difference is directly proportional to the current

• Resistivity is an intrinsic property of a conductor characterizing its ability to resist to the current