Foundations in electric circuits (Topic 3A)

Circuit symbols are graphical representations that represent electrical components in a circuit. Some of the essential circuit symbols are shown below.

It is important that you are able to recall the name and function of these circuit components for your exams.

The key functions of major electrical components are summarised below.

A circuit diagram uses standardised symbols to visually represent an electrical circuit.

Circuit diagrams can include a variety of electrical components, ranging from simple setups that consist of a cell, wires, and a resistor to more complex designs that feature combinations of resistors, capacitors, thermistors, and other elements.

Rules for circuit diagrams:

1. Use horizontal or vertical lines to represent wires only.
2. Use the standardised circuit symbols.
3. Do not leave any gaps between wires.

Drawing the direction of the current flow can be helpful, but is not essential. Current flows from the positive terminal to the negative terminal of the cell or battery.

The simple circuit below consists of a cell, an ammeter, and a resistor.

• The battery serves as a power source, providing electrical energy to drive electrons around the circuit.

• The ammeter measures the current travelling through the wires.

• The resistor is used to control the amount of current travelling through the circuit.

It is important to note that some of the electrical energy travelling through the resistor and wires is dissipated as heat.

This simple circuit setup enables you to measure the current flowing through a resistor when a specific voltage is applied by the battery. This can be used to measure voltage if the resistance is known, or to measure resistance if the voltage is known.

The simple circuit below consists of a cell, a switch, and a lamp.

• The battery serves as a power source, providing electrical energy to drive electrons across the circuit.

• The switch prevents current from flowing through it when it is closed.

• The lamp converts electrical energy into light energy.

This simple circuit setup enables a light to be turned on and off using a switch.

Particles like protons and electrons carry a physical property known as electric charge, which is positive for protons and negative for electrons. Other particles, such as neutrons, do not carry any electric charge.

• Charged objects exert electrostatic forces on each other.
• Charge can be positive or negative.
  • Like charges repel.
  • Opposite charges attract.

Electric current is the flow of charge carriers. An electric current in a metal is due to the flow of electrons.

Metals consist of a regular lattice of positively charged metal ions with a sea of delocalised electrons, which are able to move between the ions.

Most of the electrons in a metal are localised to the atoms and do not contribute to an electric current.

Applying a voltage to a metal wire causes the delocalised electrons to move through the wire from the negative end to the positive end.

Conventional current is defined as the direction in which positive charges flow. Conventional current was defined before the discovery of the electron.

Even if the current flow is due to electrons, conventional current is still treated as flowing from a positive terminal to a negative terminal. Electron current is in the opposite direction to conventional current.

For example, the current in metals is due to electrons, which flow in the opposite direction to conventional current.

Current is measured in electric circuits using ammeters. They can be assumed to have zero resistance, meaning they have no effect on the current flow.

Ammeters are placed in series with a component to measure the current flowing through it.

The circuit symbol for an ammeter is a circle with a capital A in the centre as shown below.

Potential difference is defined as the energy transferred per unit charge.

When a circuit component has a potential difference across it, electrical energy is transferred from the power supply to the charge carriers and then to the component. The greater the difference in electric potential between the battery terminals, the more energy each coulomb of charge receives as it passes through the cell.

An example of energy transfer is a filament bulb connected to a battery. The bulb converts electrical energy into light and thermal energy. A battery with a higher potential difference between its positive and negative terminals supplies more energy per unit charge, so it charges the bulb with more energy each second, making it shine more brightly.

The potential difference across a component in a circuit is measured by connecting a voltmeter in parallel to the component. The circuit symbol for a voltmeter is a circle with a capital V in the centre.

For example, the diagram below shows a voltmeter connected in parallel to a filament bulb.

A voltmeter can be assumed to have infinite resistance, so that no current flows through it when it is connected in parallel to a component.

Note that in reality, a very small, non-zero current must flow through the voltmeter. This current is required for the voltmeter to function and measure the energy carried by each charge.

Resistance is the measure of how easily current can flow through an electrical component. Resistance is the opposition to the flow of electric charge. A higher resistance means that less current can flow for a given applied voltage.

It is important to note that you will only see this symbol (the box shape for a fixed resistor) in exam questions.

It is useful to note that you may sometimes see a resistor drawn as a jagged line, shown in the diagram on the right, but the rectangular symbol is the most common.

An ohmic conductor has a linear characteristic current–voltage graph. A rearranged form of Ohm’s law states that:

The left-hand side of the equation is equal to the gradient of a linear graph. Therefore, the gradient of an graph for a conductor is equal to the reciprocal of its resistance. The steeper the gradient of the graph, the lower the resistance of the conductor.

The general equation of a straight line is:

Where:

• is the gradient, and
• is the Y-intercept.

Setting and gives:

Comparing this equation to Ohm’s law confirms that , but also shows that when : the graph of an ohmic conductor passes through the origin.

It is important to note that exam questions can be set where either or is on the horizontal axis of the characteristic graph

Kirchhoff’s first law can be expressed mathematically:

Where:

• The symbol means ‘sum of’,
• is the curruent into the junction of an electric circuit, and
• is the curruent out of the junction.

The junction below has currents of and flowing into it:

Using Kirchhoff’s first law, this must be equal to the current flowing out of the junction, so

In any circuit loop, potential rises across batteries or cells by their EMF and drops across components by their resistance multiplied by the current flowing through them.

The sum of the EMF is equal to the sum of the p.d. in any loop of a circuit.

If the direction of the current is negative in any part of a loop, then the direction of the p.d. is negative.

Only the red parts of the circuit are the loop being analysed in the examples above. Black sections are part of the real circuit but aren’t used in that loop’s equation.

Curved arrows show the direction you’re tracing the loop, not the actual current direction.

Trace with the current and the p.d. is positive; trace against it and the p.d. is negative, even though the resistor’s real p.d. hasn’t changed.

Kirchhoff’s first law states that the sum of the current flowing into a junction is equal to the current flowing out of a junction.

In a series circuit:

• the current through each resistor is the same.
• the sum of the voltages across the resistors is equal to the total voltage.

The total resistance of two or more resistors in series is given by:

In a parallel circuit:

• the voltage across each resistor is the same,
• the sum of the currents through the resistors is equal to the total current.

The total resistance of two or more resistors in parallel is given by:

Some circuits contain both series (denoted in the diagram as ) and parallel combinations. In such cases, the equations for series and parallel resistors can be combined.

There are three common equations for electrical power. To select the correct electrical power equation, first identify which quantities are given in the question.

These equations are all equivalent, but selecting the correct one first avoids unnecessary rearranging.

Avoid common exam pitfalls such as introducing extra steps or using incorrect formulas. These errors not only waste valuable time but also increase the risk of algebraic or unit mistakes.

A quick check of the given quantities in the question should immediately determine the correct equation.

In a series circuit with two unequal resistors, the current is the same through all components. The power dissipated in a component is given by:

Since the current is the same, the power dissipated in the component is directly proportional to the resistance of the component. Therefore, the component with the larger resistance dissipates more power.

The resistor with the greater resistance converts more electrical energy into heat and transfers it to the environment each second, thereby raising the temperature.

In a parallel circuit with two unequal resistors, the potential difference across each component is the same. The power dissipated in a component is given by:

Since the potential difference is the same, the power dissipated in the component is inversely proportional to the resistance of the component. Therefore, the component with the smaller resistance dissipates more power.

The resistor with the smaller resistance dissipates more power, resulting in a higher rate of electrical energy transfer to the surroundings and consequently, greater heating.

Fixed resistors are ohmic conductors. The curve of a fixed resistor shows a linear relationship.

The resistance of a fixed resistor is equal to the inverse of the gradient of the curve. Therefore, a steeper graph means a lower resistance.

A filament lamp is a non-ohmic conductor:

At low current, a filament lamp is an ohmic conductor and has a linear curve. However, the filament lamp becomes a non-ohmic conductor at higher current:

• The temperature of a filament lamp increases with current.
• As a filament lamp heats up, its metal ions vibrate more, which increases the resistance.
• A large resistance leads to the gradient of the curve decreasing.

A thermistor is a non-ohmic conductor. The resistance of a thermistor depends on its temperature. For a negative temperature coefficient (NTC) thermistor, the resistance decreases as the temperature increases.

When the temperature of a thermistor increases, additional charge carriers are released which can contribute to a current, decreasing the resistance (since resistance is opposition to current flow).

The curve for a thermistor is linear at low currents. At high current, a thermistor’s temperature increases, decreasing its resistance, causing the gradient of the curve to become steeper.

The temperature dependence of thermistors makes them useful for thermometers and thermostats.

A diode is a non-ohmic conductor. Diodes only allow current to flow in one direction.

The two circuits above show how the curve for a diode relates to how it is connected in a circuit:

• Forward bias
  • When the diode arrow is pointing in the direction from the positive terminal to the negative terminal, current flows through the circuit.
  • For current to flow, the applied voltage must be greater than the threshold voltage, which is normally
  • In the circuit diagrams above, the lamp will turn on when the diode is connected in forward bias.
• Reverse bias
  • When the diode ‘arrow’ is pointing from the negative terminal to the positive terminal, no current can flow.
  • The lamp does not turn on.

In forward bias, the diode has a small resistance, which can lead to very large currents flowing through the circuit. To prevent damage to the circuit components, a fixed resistor is included to reduce the current.

A light-emitting diode (LED) emits monochromatic light in forward bias. They are made from semiconducting materials.

In forward bias, a current flows through the LED and electrical energy is converted to light energy.

The threshold voltage is the minimum forward voltage required for the LED to start conducting. It corresponds to the energy needed for electrons to cross the energy band gap in the semiconductor material and emit photons. Different LED materials have different band gap energies, which determine both the colour of light emitted and the threshold voltage. LEDs that emit shorter-wavelength light have larger band gaps and therefore higher threshold voltages.

It is useful to note that white LEDs often use a blue LED coated with a phosphor that converts some of the blue light into other wavelengths, resulting in white light. Because of the large energy gap involved, white LEDs typically have the highest threshold voltage among visible LEDs.

The resistivity of a metal can be determined using the following circuit components in the setup below:

• A flying lead is used to adjust the length of a current-carrying test wire being measured.
• A voltmeter is connected in parallel to the test wire using the flying lead to measure the potential difference across it.
• An ammeter is connected in series to the test wire to measure the current flowing through it.
• A power source supplies a voltage to the circuit.

The potential difference across the test wire and the current through it are measured, allowing the resistance to be calculated by Ohm’s law:

The equation for the resistance of a wire can be rearranged for resistivity :

A graph of resistance against length will have a gradient equal to the resistivity of the material divided by the cross-sectional area:

Which can then be multiplied by the cross-sectional area of the wire to find the resistivity.

The graph below shows the resistance against length plots for copper and aluminium wires of the same cross-sectional area.

The gradient for the aluminium wire is steeper than that of the copper wire, indicating that aluminium has a higher resistivity than copper.

When a potential difference is applied across the ends of a wire, by the terminals of a cell or battery, electrons move through the wire.

Electrons move around a circuit from the negative terminal of a cell or battery to the positive terminal.

It is important to note that conventional current is the flow of positive charge, which is in the opposite direction to the flow of negatively charged electrons. This is called electron current.

As electrons move through a wire, they collide with static metal ions, causing them to be scattered in random directions. Electrons can also collide with defects in the wire.

Despite the collisions, the electric force due to the potential difference at the ends of the wires still causes a net movement of electrons through the wire. This is called electron drift.

• The velocity of the electrons is referred to as their mean drift velocity.
• Electrons move through wires much more slowly than through free space.

An example of this is the standard copper wire used in the laboratory carrying a current, electrons move as slowly as

The current equation shows that the following properties will result in a greater current through a wire:

• Larger area : There is more space for electrons to flow through the wire.
• Greater electron density : There are more electrons to flow through the wire.
• Higher mean drift velocity : Due to the increased rate at which electrons flow through any point in the wire.

The number density is the number of electrons per cubic metre of material is measured in SI units of

A greater number of electrons in a given volume means more electrons are available to carry current. Therefore, a higher value of results in a better electrical conductivity.

Materials are classified in terms of their number density and hence their electrical conductivity:

• Metals like copper have a high number density: generally in the range to Metals are good conductors of electricity.
• Semiconductors such as silicon have an intermediate number density: generally in the range Semiconductors do not conduct electricity as well as metals, but their number density can be increased by raising their temperature.
• Insulators have a low number density – practically zero – and do not conduct electricity.

Some examples of the value for different common materials are listed in the table below.