Current, Resistance & Potential Difference

Electric Current

Electric current is the rate of flow of electric charge through a conductor or circuit. It tells us how much charge passes a point in the circuit every second.

Current is measured in amperes (A), where 1 ampere means 1 coulomb of charge passes per second.

In metals, current is caused by the flow of electrons moving through the lattice of positive metal ions. In other materials, such as electrolytes, current can be due to ions moving.

The symbol for current is I.

For instance, if 10 coulombs of charge pass through a wire in 5 seconds, the current is:

$\text{Current} = \frac{\text{Charge}}{\text{Time}} = \frac{10\, \text{C}}{5\, \text{s}} = 2\, \text{A}$

Potential Difference (Voltage)

Potential difference, often called voltage, is the energy transferred per unit charge as electric charge moves through a component.

It tells us how much energy each coulomb of charge gains or loses when passing through a component.

The unit of potential difference is the volt (V), where 1 volt = 1 joule per coulomb.

The symbol for potential difference is V.

Mathematically,

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

where $E$ is the energy transferred in joules (J) and $Q$ is the charge in coulombs (C).

For example, if 20 J of energy is transferred when 5 C of charge pass through a component, the potential difference is:

$$V = \frac{20}{5} = 4\, \text{V}$$

Resistance

Resistance is a measure of how difficult it is for current to flow through a component or material.

It causes electrical energy to be converted to other forms, like heat, as current flows.

The unit of resistance is the ohm (\u03A9).

The symbol for resistance is R.

Factors affecting resistance include:

• Material: Some materials conduct electricity better (lower resistance), e.g. copper vs. nichrome.
• Length: Longer wires have higher resistance because electrons collide more often.
• Cross-sectional area: Thicker wires have lower resistance as there is more space for electrons to flow.
• Temperature: For most metals, resistance increases with temperature as atoms vibrate more, making electron flow harder.

For example, a long thin wire of nichrome will have a higher resistance than a short thick copper wire.

Ohm's Law

Ohm's law states that, for some components, the current flowing through the component is directly proportional to the potential difference across it, provided the temperature remains constant.

This means:

$$V = IR$$

where:

• $V$ is the potential difference in volts (V)
• $I$ is the current in amperes (A)
• $R$ is the resistance in ohms (\u03A9)

Components that obey Ohm's law are called ohmic conductors. Their I 6V graphs are straight lines through the origin, showing a constant resistance.

Non-ohmic components, such as filament lamps or diodes, do not have a constant resistance, so their I 6V graphs are curved.

For example, a resistor with a resistance of 4 \u03A9 carrying a current of 3 A will have a potential difference of:

$$V = 3 \times 4 = 12\, \text{V}$$