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5.1 - Potential Difference, Current and Resistance

A model can help us to understand how current works in an electric circuit.

What do the pizza shop and the house of party-goers represent?

In this model, the moped riders represent the flow of charge and the pizzas represent the electrical energy carried around the circuit.

How can we model electric circuits?

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Potential DifferenceThe easiest way to think about what batteries do is to use a water analogy.

Batteries ‘lift’ charges (Q) to a higher Potential (V).

There is a Potential Difference (V) between one end of the battery and the other.

Batteries store Potential Energy as Chemical Energy.

Battery Voltage Simulator on PhET website

http://phet.colorado.edu/en/simulation/battery-voltage or click the pictures

This simulator shows another way of imaging what batteries do.

Water model of a circuit

This page has embedded flash which only works in Powerpoint.

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What are Coulombs?

Because charge is made out of electrons which are very small, it seems silly to measure charge in electrons because the numbers of charges that go round a circuit would be billions and billions.

Instead Charge (Q) is measured in Coulombs (C)

Using this scale 1 electron is only: 1.6x10-19 C

1 Coulomb is:

6,250,000,000,000,000,000 electrons

Remember this number

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Current (I)Batteries ‘lift’ charges to a higher potential.

The charges then flow around the circuit.

The flow of charges per second is called:current.

1C/s𝐼=𝑄𝑡

Charge

Time

Current

This way of representing the direction of current is called Conventional Current.

It is now know that charge is carried by electrons, flowing from the negative terminal to the positive terminal. This is called electron flow.

Before the discovery of the electron, scientists assumed that current was due to positively-charged particles moving from the positive terminal around a circuit to the negative terminal.

Today, both conventional current and electron flow can be used to represent the direction of current.

What is conventional current?

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Potential Difference (V) ..sometimes known as Voltage

Batteries ‘lift’ charges to a higher potential.

There is a Potential Difference because each coulomb of charge has a different potential energy at either end of the battery.

𝑉=𝐸𝑄

Potential Difference

Energy

Charge

1J/C

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Electromotive ForcePotential Difference (V)The total amount of Chemical Energy in the battery transferred to Electrical Energy by each Coulomb of charge

Electromotive Force(EMF) and Potential Difference:

The total amount of Electrical Energy transferred to Heat by each Coulomb of charge

11Website Link or click on the picture

How do metals conduct electricity?

The delocalized electrons are free to flow through the metal and so carry a current.

Insulating materials do not contain free electrons and so current is unable to flow.

Ionic solutions are also able to conduct electricity because they have mobile charge-carrying particles.

It is the delocalized electrons involved in metallic bonding that allow metals to conduct electricity.

delocalized electrons

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Resistance (R)Some materials are better than others at allowing current to flow.

A material that doesn’t let much current flow for a given Potential Difference is said to have a high Resistance.

This resistance depends on the material and the dimensions of the conductor

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Factors affecting Resistance on PhET website

http://phet.colorado.edu/sims/resistance-in-a-wire/resistance-in-a-wire_en.html or click the picture.

Why does Length affect resistance?

The affect of length of a wire on resistance can be understood by looking at the atomic structure.

Resistance is caused by electrons colliding with metal ions. When the length of the wire is increased, the electrons have to travel further. So the chance of collisions will increase, causing the resistance to increase.

Why does Cross Sectional Area affect resistance?

Increasing the thickness of a wire increases the cross sectional surface area that the electrons can flow through.

In thick materials the charge carrying particles are able to move through the conductor more easily, reducing resistance.

This decreases the chance of collisions with metal ions.

What is Resistivity?

Resistivity is just a property of the conductor.

Every material has a resistivity.

It is actually the resistance of a 1m long piece of wire with a cross-sectional area of 1m2.

As you can imagine this is always a very low number.

For Copper ρ = 1.72 x 10-8 Ωm

ρ=𝑅𝐴𝐿

Units = Ωm

18http://phet.colorado.edu/en/simulation/battery-resistor-circuit

Battery Resistance Simulator on PhET website

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Ohms Law

Ohms law relates the current flowing through a conductor with the potential difference across it.

V∝I V=IRR is the constant of proportionality between I and V

20Both these circuits have 2 Volts per Amp or a resistance of 2Ω

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Ohms Law simulator on the PhET website

http://phet.colorado.edu/sims/ohms-law/ohms-law_en.html or click on the picture

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Ohmic Conductor

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Non-Ohmic Conductor

The reason for this is that as the lightbulb gets hot there are more collisions between the atoms so the resistance increases