Chapter 27: Current and ResistanceReading assignment: Chapter 27

Homework 27.1, due Wednesday, March 4: OQ1, 5, 14

Homework 27.2, due Friday, March 6: OQ3, OQ6, 15, 21, 25, 26, 31, 33, 39, 44, 48, 53

• Begin our study of charges in motion --> electric current

• Electrodynamics

• Invention of battery, Alessandro Volta, 1800 --> production of steady electric current

• Electrical current and circuits are omnipresent in today’s technological world

• Electric current, Ohm’s law, resistance, resistivity, electric power

Batteries

• There is a potential difference (voltage) between the terminals of

a battery:

• Series connection:

• Voltages add up in a series connection. The voltage between the

ends of three 1.5 V batteries connected in series is 3·1.5V = 4.5V.

• Symbol of battery in a circuit:

+- +- +-

Electric current• When a continuous conducting path is

connected between the terminals of a

battery, we have an electrical circuit.

• When such a circuit is formed, charge can flow through the wires of the circuit, from one terminal of the battery to the other. A flow of charge, such as this is called an electrical current.

Symbol for battery

• The electrical current, I, in a wire is defined as the amount of charge that passes through it per unit time.

QI

t

DQ is the amount of charge that passes through the conductor at any location during time interval Dt.

• The direction of current is the direction in which positive charges flow

• Unit of electrical current is Ampere (1A) (Coulomb/second).

dQI

dt

Instantaneous current

(a) (b) (c)

- --

How to connect a battery

What’s wrong with each of the

schemes shown in the Figure for

lighting a flashlight with a

flashlight battery and a single wire?

(a) There is no loop for the current to flow around

(b) There is loop to and from the light bulb, but there is no potential difference

(c) Nothing wrong here. The bulb will light up.

i-clicker:

Current flow of charge. A steady current of 2.5 A flows in a wire for 4.0 minutes.

1) How much charge passes through any point in the circuit?

A) 0 C C) 600 C

B) 10 C D) 1000 C

2) How many electrons would this be?

Ohm’s Law• To produce an electrical current I in a wire, a difference in potential V is required (set

up by a battery power supply or outlet).

• Ohm’s law: The current in the wire is proportional to the potential difference applied to its ends:

I V The amount of current flowing in a wire for a given voltage depends on the resistance of the wire, R. The higher the resistance the less current will flow for a given voltage.

VI

R

Or: V IR Ohm’s Law

Resistance: Unit of resistance: 1 Ohm (1 W)V

RI

Georg Simon Ohm1789 – 1854

White board example

Ohm’s law. Flashbulb light resistance.

A small light bulb draws 300 mA from its 1.5 V battery

(A) What is the resistance of the light bulb?

(B) If the voltage dropped to 1.2 V how would the current change?

How to read the code (four band code):• First find the tolerance band, it will typically be gold ( 5%)

and sometimes silver (10%).• Starting from the other end, identify the first band - write

down the number associated with that color. • Now 'read' the next color• Now read the third or 'multiplier' band• If the resistor has one more band past the tolerance band it is a

quality band. Read the number as the '% failure rate per 1000 hour' This is rated assuming full wattage being applied to the resistors.

Resistors

• All electric devices offer resistance to the flow of current (filaments of light bulbs or electric heaters)

• Resistors are used to control the amount of current. They have a resistance ranging from less than on Ohm to millions of Ohms.

• Symbol in a circuit is

Resistivity

• The resistance of a wire is proportional to its cross section A and inversely proportional to its length L.

A

LR

• The proportionality constant r is called the resistivity.

• It depends on the material and has units of W·m.

• There is a huge range of values across different materials.

• Typically metals (the best is silver r = 1.6x10-8 W·m) have a very low resistivity (are good conductors).

• Insulators have a very high resistivity (glass: 109 – 1010 W·m).

Effect of temperature on resistance

00 1 TTT

• Typically (but not always!) the resistivity (and thus the resistance) of metals increases with increasing temperature.

• At higher temperatures the atoms are moving more rapidly and thus interfere with the flow of the electrons.

• a can be negative for semiconductors, i.e. resistance decreases with increasing temperature! Why?

00 1 TTRRT

RT and R0 are resistance at temperature T and reference temperature T0 (usually 20°C)

a is the temperature coefficient of resistivity (see Table 27-2)

White board example

Resistance thermometer. The variation in electrical resistance with

temperature can be used to make precise temperature measurements.

Suppose at 20oC the resistance of a platinum resistance thermometer is

164.2 W. When placed in a particular solution, the resistance is 187.4 .W

What is the temperature of this solution?

Electric power• Electric energy is useful, because it can be easily transformed into other

forms of energy (heat, light, mechanical).

• Electrons loose all their energy (potential) as they travel through the circuit from one terminal of the battery to the other terminal

• Remember: electric potential energy: DUel = QDV)

energyP = power =

time

Q V

t

P I V

2

2

( )P I V I IR I R

V VP I V V

R R

• By using Ohm’s law, V = IR, the power in a resistance can be written as:

Power is measured in Watt

Black board example

Electric heater. An electric heater draws 15.0 A on a 120V line

(regular household outlet).

A) How much power does it us?

B) How much does it cost to operate it for 90 hours if the

electric company charges 10.5 cents per kWh? (Assume

steady current flow in one direction)

Lightning bolt.

In a typical lightning event, 109 J of energy are transferred

across a potential difference of 5 x 107 V during a time

interval of 0.2 seconds.

Use this information to estimate

A) the total amount of charge transferred,

B) the current

C) and the average power over the 0.2 seconds.

Black board example

Microscopic model of current and Ohm’s law again

avg dI nqv AI … currentn … density of charge carriersq … charge per carriervd … drift velocityA … cross-sectional area

J E Ohm’s law

J… current density, I/As… conductivity, s = 1/r; r… resistivity, (material constant)E … electric field

ReviewQ

It

dQ

Idt

V IR Ohm’s Law (common def.):

A

LR

00 1 TTT 00 1 TTRRT

energyP = power =

time

Q V

t

P I V

2

2

( )P I V I IR I R

V VP I V V

R R

avg dI nqv A J EMicroscopic definition ofcurrent, I, and Ohm’s law

Definition of current:

Resistance of a wire:

Temp. dependence of

resistivity r, Resistance, R: