Electric Current and Resistance

Here below an English/ Italian glossary, that we will fill during our activities

Current

Circuit

Charge

Potential

Voltage Voltaggio = ddp

Battery

Switch

Net

Wire

Copper

Ammeter/Voltmeter

Drift

Plate piastra

Positive/negative terminal

electron

Electric field

Resistor

Resistance

Series/parallel

Which of these connections could work to light the bulb?

The Central Concept: Closed Circuit

circuit diagramcircuit diagram

cell switch

lamp

wires

Scientists usually draw electric circuits using symbols;

Remember: Electric Potential Energy- Two Unlike Charges

Higher Potential Energy

Lower Potential Energy

+

-

•To cause movement of a charge, there must be a potential difference.

Closing the switch establishes a potential difference (voltage) and an electric field in the circuit.

• Electrons flow in a net direction away from the (-) terminal.

High PotentialLow

Potential

Conventional Current• By tradition,

direction in which “positive charges” would flow.

• Direction is opposite of electron flow.

Question:

What is required in order to have an electric current flow in a circuit?

Answers:1. A voltage source.

2. The circuit must be closed.

Battery (Chemical Cell):

• A device that converts chemical energy to electricity.

• A battery provides a potential energy difference (voltage source).

Electric Current:

• The flow of electric charges.

Electric Current, I

I = q

t

• Rate

• Unit: Coulomb / sec = Ampere (A)

• Andre Ampere (1775-1836)

Conventional current has the direction that the (+) charges

would have in the circuit.

• Direct Current

• DC• Provided by

batteries

• Alternating Current

• AC• Provided by power

companies

TWO TYPES OF CURRENT

MEASUREMENT DEVICES

:1) Ammeter

• Measures electric current.

• Must be placed in series.

2) Voltmeter• Measures the

voltage between two points in an electric circuit.

• Must be connected in parallel.

Example:

• What charge flows through a cross sectional area of a wire in 10min, if the ammeter measures a current of 5mA?

• Answer: 3C

RESISTANCEIt is known from experiment that the current flowing in a conductor is directly proportional to the potential difference across it.

The constant of proportionality, R, is called the RESISTANCE

R = V / I

(resistance equals the ratio of voltage to current)

Unit: Ohm (Ω) 1 Ω = 1 V/A

Ohm’s Law

I = V / RI = V / R

Georg Simon Ohm (1787-

1854)

I = Current (Amperes) (amps)V = Voltage (Volts)R = Resistance (ohms)

I

V

Gradient RV

I 1

A device that obeys Ohm’s Law is called a ohmic resistor(its resistance does not depend on the voltage)

The current through an ohmic conductor is:•directly proportional to the voltage across it (over a limited range of V)

(more voltage more current)

•inversely proportional to the resistance of the conductor(the greater the resistance the less the current)

But what is resistance?It is a measure of how much a conductor It is a measure of how much a conductor impedes the flow of currentimpedes the flow of current

At the molecular level, electrons undergo frequent collisions with the ions of materials.

The higher the number of collisions, the higher the resistance of the material is.

It’s a sort of friction, an opposition to the flow of current

Resistor

• An object that has a given resistance.

RESISTORS

Colour codes are used to identify resistance value

Circuit symbol

(or the “zig-zag symbol)R

The ResistorColour Code

Colour Number

Black 0

Brown 1

Red 2

Orange 3

Yellow 4

Green 5

Blue 6

Violet 7

Grey 8

White 9

The four colour code bands are at one end of the component.

Counting from the end, the first three (or sometimes four or five)

bands give the resistance value and the last the tolerance

TOLERANCES

BROWN 1%

RED 2%

GOLD 5%

SILVER 10%

NONE 20%

Example:

• Calculate the current through a 3 Ω resistor when a voltage of 12V is applied across it.

• Answer: 4 A

Example:

• A 6 Ω resistor has a power source of 20V across it. What will happen to the resistance if the voltage doubles?

Answer:

resistance doesn’t change!

Factors that affect resistance:

• Type of material

• Size and shape

• Temperature

ResistanceR = ρ L (a.k.a. Ohm’s 2nd law)

A

L: length of the wire

A: cross-sectional area

ρ: resistivity (inherent to material)Unit: m

RESISTIVITIES FOR CERTAIN MATERIALS AT 20°C(measured in m)

Silver 1.6 × 10-8

Copper 1.7 × 10-8

Aluminium 2.8 × 10-8

Tungsten 5.6 × 10-8

Constantan

(alloy of copper and nickel) 49 × 10-8

Nichrome

(alloy of nickel, iron & chromium) 100 × 10-8

Graphite (3 - 60) × 10-5

Silicon 0.1 – 60 (semiconductor)

Germanium (1 - 500) × 10-3

Pyrex glass 1012 (insulator)

The table of resistivity values shows that, although silver has a low resistivity, it is expensive to use in electrical circuits.

Copper is the preferred metal although aluminum is commonly used in electricity transmission cables because of its lower density.

What is the best material?

Example:

Determine the resistance of a piece of copper wire that is 10.0 m long and 1.2 mm in diameter.

Solution

The resistance, R, is given by the formula

R = ρL / A, where A = πr2.

This means that

R = (1.7 × 10-8 Ωm) (10.0 m) / π(6.0 × 10-4)2 m2 = 0.150 Ω.

The resistance of the copper wire is 0.15 Ω.

Question:

• What happens to the resistance when the length is doubled and the area is quadrupled?

Answer: It changes by 1/2

Temperature Dependence of Resistance

The resistance of a material increases with temperature because of the thermal agitation of the atoms it contains, and this impedes the movement of electrons that make up the current.

Resistance increases because resistivity increases, as shown in this formula:

t = 20[1 + (t -20°)]

where 20 equals the resistivity at 20 °C, t is the resistivity at some temperature, t °C, above the reference temperature, and is the temperature coefficient for the material being used.

SUPERCONDUCTIVITY

One interesting phenomenon of the effect of temperature

on resistance is superconductivity.

In 1911, H. Kammerlingh Onnes found that mercury loses all its resistance abruptly at a critical temperature of 4.1 K.

When a material attains zero resistance at some criticalWhen a material attains zero resistance at some critical

temperature, it is called a superconductor. temperature, it is called a superconductor.

The possibility of having a material that has an induced electric current that lasts forever has become a topic for research physicists.

Just think of the energy saving if the perfect superconductor is found that can give zero resistance at room temperature.

POWER DISSIPATION INRESISTORS

Electric power is the rate at which energy is supplied to or used by a device.

It is measured in J/ s called watts (W).

When a steady current is flowing through a load such as a resistor, it dissipates energy in it.

This energy is equal to the potential energy lost by the charge as it moves through the potential difference that exists between the terminals

of the load.

Some possible power ratings for household appliances

If a vacuum cleaner has a power rating of 1500 W, it means it is converting electrical energy to mechanical, sound and heat energy at the rate of 1500 J/s.

A 60 W light globe converts electrical energy to light and heat energy at the rate of 60 J/s .

Electric power

Basic definition of power: P = W/ t Work / time

We know that W = q V and q = I tP = q V/t = I t V/ t P = V I(V is the voltage)

And applying Ohm’s law: P= R I2 = V2 / R

UNIT OF ELECTRIC ENERGYThe commercial unit of electrical energy is the kilowatthour (kW h).

It is the energy consumed when 1 kW of It is the energy consumed when 1 kW of power is used for one hour. power is used for one hour. The consumer has to pay a certain cost per kilowatt-hour.

--------------------------

Question: How many Joules in a kWh?

1 kWh = 1000 W x 3600 s = 3600000 J

= 3.6 x 106 J

HEATING EFFECT OF A CURRENT(Effetto Joule)

It was investigated in 1841 by James Joule.

He was able to demonstrate that by supplying electrical energy to a high resistance coil of wire this energy could be converted to thermal energy.

V × I × t = m× c × ΔT

electric energy heat = infrared radiation

ExampleAn electrical appliance is rated as 2.5 kW, 240 V.(a) Determine the current needed for it to operate.(b) Calculate the energy it would consume in 2.0 hours.Solution:(a)Given that P = 2.5 × 103 and V = 240 V, we use the formula, P = IV I = P/W = …10.4So I = 1.0 × 101 A.(b) Next, we use the formula W = VIt, so thatW =(240 V) x(10.4 A)x 7.2 103 s = = 1.8 × 107 JThe energy consumed is 1.8 × 107J.

Exercises

1) The element of an electric jug has a resistance of 60 Ω and draws a current of 3.0 A. Determine by

how much the temperature of 5.0 kg of water will

rise if it is on for 6 minutes.

2) Calculate the cost to heat 200 kg of water from

12°C to its boiling point if power costs 14 cents

per kilowatt-hour.