A-level Physics/Electrons, Waves and Photons/Electric current

Electricity is useful because we can easily transform electrical energy to other forms of energy such as light, sound and heat. Electricity is transferred from place to place by wires as an electric current.

Current and Charge

Electric current is the flow of charged particles, usually electrons, around a circuit. Metals are good conductors of electricity because they have free electrons that can move around easily.

Current is measured in amperes.

Charged particles have a charge which is either positive or negative. The strength of a charge can be found using the formula:

$Q=I\times t$

where Q is the quantity of charge in coulombs, I is the current in amps, and t is the time in seconds

We can use this formula to define the coulomb:

One coulomb is the amount of charge which flows past a point when a current of 1 ampere flows for 1 second

Electron flow

When you attach a battery to a small bulb with wires, you would say that the current is flowing from the positive terminal of the battery to the negative one. This is called conventional current. The electrons, however, flow from the negative terminal to the positive. This electron flow is in the opposite direction to the conventional current, and care must be taken to not confuse the two. When we just say current it is assumed that we are talking about conventional current.

The reason for this is that the direction of conventional current was chosen before people knew what was happening inside a conductor when a current flows.

In A-level, charge in coulombs is the product of current in amperes by the time in seconds.

Resistance

Any component with electrical resistance opposes the flow of an electrical current.

Electrical Resistance

In an electrical circuit, current flows around it. Each component in the circuit has a resistance, which resists the flow of the current.

The voltage that you get from the power supply can be simply described as the "push" given to the electrons to go around the circuit.

It would then make sense to say that the greater the voltage, the greater the current, and the greater the resistance, the lower the current. The current flowing around the circuit could then be written as the equation:

$I={\frac {V}{R}}$.

For example, if you were to connect a 9 volt power supply to a 3 Ω (read as 3 ohm) resistor, you could use the formula above to find the current. $I={\frac {9}{3}}$, so $I=3A$.

A particular arrangement of this formula is used to define resistance and the ohm.

$R={\frac {V}{I}}$.

This says that the resistance of a component is the voltage across it for every unit of current flowing through it. More formally this can be written as:

The resistance of a component in a circuit is the ratio of the voltage across that component to the current in it.

The unit of resistance, the ohm (Ω), is defined so that one ohm is the resistance of a component that has a voltage of 1 volt across it for every amp of current flowing through it. In other words, one ohm is one volt per amp.

Ohm's Law

In many components, the voltage across it is proportional to the current flowing through it. You can make this observation on a circuit with a resistor of a known resistance, a voltmeter, an ammeter, and a power supply with a variable voltage. As you increase the voltage, the current will also increase. You will come to the conclusion that $V\propto I$, with the constant of proportionality equal to $R$. This gives us $V=IR$, an arrangement of the familiar formula.

Components where $V\propto I$, are known as ohmic conductors, and have a constant resistance. They are said to follow Ohm's law, which states that:

If the source voltage remains constant, the flow of current is inversely proportional to resistance.

      OR

If the temperature remains constant, the current flowing through a conductor is directly proportional to the potential difference across it.

Note that not all components are ohmic conductors, and can have varying values of resistance. You will have to use the formula $R={\frac {V}{I}}$ to find the resistance for specific values of $V$ and $I$.

Below you can see 3 graphs with current on the vertical axis, and voltage on the horizontal axis. Where the graph is a straight line, the voltage is proportional to the current. Therefore, only the metallic conductor is an ohmic conductor.

A diode and a filament lamp are two examples of non-ohmic conductors. The diode is designed to only allow current through in one direction, hence the use of negative values on its graph. The filament lamp doesn't have a constant temperature, which according to Ohm's law is required for a component to be an ohmic conductor. Instead, it heats up as a current passes through it, which has an effect on the resistance.

Resistivity

The resistivity of a material is the property that determines its resistance for a unit length and unit cross sectional area of that material. Copper, for example, is a better conductor than lead, in other words lead has a higher resistivity than copper. You can compare different materials in this way.

Resistivity, ρ (the Greek letter rho), is defined by the equation:

$\rho ={\frac {RA}{l}}$

Where ρ is resistivity, R is the resistance, A is the cross sectional area of the material, and l is the length of the material.

The units of resistivity are Ohm-meters, Ωm.

If we rearrange the above equation so that:

$R={\frac {\rho l}{A}}$

You can see that as the length of a wire is increased, its resistance will increase, and as the cross sectional area of a wire is increased, its resistance will decrease. This is true provided that the temperature is constant, and that the same materials are always used, to make sure that the resistivity stays the same.

Voltage and Energy

Earlier, we simply said that a voltage is the "push" given to electrons, or units of charge. Now, we will take a look at voltage in terms of energy, and find a more accurate definition of the volt.

Potential Difference

When you attach a voltmeter across a component, the voltage you are measuring is a potential difference (PD). Electrical energy is being used up by the component, and so we can say that a potential difference is a voltage where the charge is losing energy. Potential difference has the symbol V.

By definition, the potential difference is the energy converted from electrical energy to other forms of energy in moving a unit of electrical charge from one point to another. So, if the PD of a resistor is say, 2V then if 3 coulomb of charges pass through it, then the energy used up is 6 Joules.

Potential difference is the energy lost per unit charge, and can be written as the following formula:

$V={\frac {W}{Q}}$

Electromotive Force

A battery provides a certain voltage to the circuit, and the electrons are gaining energy from the battery as they flow past. This voltage where the charge gains energy is called an electromotive force (EMF) and is measured in volts (V). Its symbol is ε.

EMF. is the energy gained per unit charge, and can be written as the following formula:

$E={\frac {W}{Q}}$

Both the PD and EMF are measured in volts, and one volt is equivalent to one joule per coulomb.

Electrical Energy and Power

Power is the rate at which energy is transferred, written as the formula:

$P={\frac {W}{t}}$

To find a formula for electrical power, we take the following formula for voltage and make W the subject:

$V={\frac {W}{Q}}$

$W=QV$

Then we need to divide both sides by t to get power:

${\frac {W}{t}}={\frac {QV}{t}}$

Recall that charge divided by time is current, we now have:

$P=I\times V$

From the formula above, you can see that the electrical power is simply the product of current and voltage. You can combine this with $V=IR$ to give two further equations:

$P=I^{2}R$

$P={\frac {V^{2}}{R}}$

One last formula is for energy and is derived from the formula for power:

$P={\frac {W}{t}}=IV$

$W=IVt$