What you'll learn

• How current, charge, voltage, resistance and energy are linked in circuits.
• Why series and parallel circuits are useful for different applications, including domestic lighting.
• How to calculate currents, voltages and resistances in simple series circuits.
• How current–voltage graphs are different for resistors, filament lamps and diodes.

1. Charge and current

Electric circuits transfer energy because electric charge moves around the circuit.

In solid metallic conductors, such as copper wires, the moving charges are negatively charged electrons. They drift through the metal when a voltage is applied.

The spec equation is:

charge = current × time

$$Q=I\times t$$

where $Q$ is charge in C, $I$ is current in A, and $t$ is time in s.

Rearranged:

$$I=\frac{Q}{t}$$

Conventional current is shown flowing from the positive terminal to the negative terminal. In metals, electrons actually move the opposite way.

2. Voltage and resistance

A voltage is sometimes called a potential difference. It tells you how much energy is transferred by each coulomb of charge.

Resistance is how much a component opposes the flow of current. It is measured in ohms, Ω.

The spec equation is:

voltage = current × resistance

$$V=I\times R$$

where $V$ is voltage in V, $I$ is current in A, and $R$ is resistance in Ω.

Useful rearrangements are:

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

3. Series and parallel circuits

A series circuit has one path for current. A parallel circuit has two or more branches.

Series circuits

In a series circuit:

• the current is the same through every component
• the supply voltage is shared between the components
• adding more components usually increases the total resistance, so the current decreases
• the current depends on the applied voltage and on the number and nature of the components

The “nature” of a component matters because not all components have constant resistance. For example, a filament lamp heats up and its resistance changes.

Parallel circuits

In a parallel circuit:

• the voltage across each branch is the same
• the current splits at junctions and recombines later
• components can be switched on and off independently

For two components connected in parallel:

$$V_1=V_2=V_{supply}$$

Parallel circuits are more appropriate for domestic lighting because each lamp gets the full mains voltage and one lamp failing does not stop the others working.

4. Calculating in a series circuit

For two resistive components in series:

$$R_{total}=R_1+R_2$$

The same current flows through both components, and the supply voltage is shared:

$$V_{supply}=V_1+V_2$$

5. Current at junctions

At a junction, current is conserved. This means the total current entering the junction equals the total current leaving it.

This happens because charge cannot disappear or pile up at a junction in a steady circuit.

For two branches:

$$I_{total}=I_1+I_2$$

6. Current–voltage characteristics

A current–voltage characteristic shows how current changes as voltage changes for a component.

Wires and fixed resistors

For a wire or fixed resistor at constant temperature, current is directly proportional to voltage. The graph is a straight line through the origin.

This means the resistance is constant.

Metal filament lamps

In a metal filament lamp, increasing current heats the filament. A hotter filament has greater resistance, so current does not rise as quickly as voltage.

The graph curves and becomes less steep at higher voltages.

Diodes and LEDs

A diode allows current to flow much more easily in one direction than the other. In reverse, the current is almost zero. In the forward direction, the current rises sharply after a certain voltage.

An LED, or light-emitting diode, emits light when current flows through it in the forward direction.

Lamps and LEDs can be used to indicate the presence of a current in a circuit, because they light up when current flows.

7. Investigating current–voltage graphs

To investigate how current varies with voltage, use:

• variable power supply
• component under test
• ammeter in series
• voltmeter in parallel
• switch
• connecting leads

Method:

1. Connect the circuit with the ammeter in series and the voltmeter across the component.
2. Start with a low voltage and close the switch briefly.
3. Record the voltage and current.
4. Increase the voltage in steps and repeat.
5. Reverse the supply connections if negative voltage readings are needed.
6. Plot current on the y-axis against voltage on the x-axis.

The independent variable is voltage. The dependent variable is current. Important control variables include the component used and, for a resistor or wire, the temperature.

To reduce errors, switch off between readings to reduce heating, avoid loose connections, and do not use currents large enough to damage a diode or LED.

8. LDRs and thermistors

Some components are designed so their resistance changes with conditions.

An LDR, or light-dependent resistor, has lower resistance when illumination increases.

A thermistor used at IGCSE is usually an NTC thermistor: its resistance decreases as temperature increases.

With a fixed supply voltage, lowering the resistance increases the current. That is why LDRs and thermistors are useful in sensing circuits.

9. Energy transferred by charge

Voltage links charge to energy.

So a component with a voltage of 6 V transfers 6 J of energy for every coulomb of charge that passes through it.

The spec equation is:

energy transferred = charge × voltage

$$E=Q\times V$$

where $E$ is energy transferred in J, $Q$ is charge in C, and $V$ is voltage in V.