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# Circuits

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We are going to move on to circuits and their components. The following symbols are used to represent the circuit components that are commonly used in physics.

You should be familiar with these symbols as you will see and may have to use these symbols, or slight variations of them, in exam questions about electricity and circuits.

Electrical circuits always include a source of electrical energy to provide the voltage, wires to provide the path for the current to travel along and a component which can be used to show that the current is being carried around the circuit. Lamps and light emitting diodes (LEDs) are both examples of components which can be used to indicate the presence of a current in a circuit.

Both of these components will only light up or glow when a current is flowing through them. If the components are connected into the circuit but do not glow, this indicates that a current is not flowing and there must be either a break in the wire or that there is no voltage pushing the electrons around the circuit.

### Series and parallel circuits and their applications

Electrical circuits can be connected in series or parallel. These distinct types of circuits have key similarities and differences which make them appropriate for different uses. You must be able to explain why a series or parallel circuit would be more appropriate for particular applications.

#### Series circuits

In a series circuit the components are connected one after the other in a line. The current that flows through each component is always equal regardless of their position in the circuit. The diagram below shows an example of a series circuit:

The electricity travels along all of the wires in the circuit. This means that the electricity has to pass through every component in the circuit and back to the starting point. If one component in a series circuit is removed or disconnected, the circuit will be broken and electricity can no longer flow.

For example, consider a set of Christmas tree lights connected in a series circuit. If one of the bulbs broke, the electricity cannot flow through to the next bulb. The circuit would be broken and none of the lights would light up. It would therefore be very difficult to know which bulb was faulty. It is clear to see why a series circuit would be a poor choice for domestic lighting!

#### Parallel circuits

In a parallel circuit each component can be placed onto separate loops which are parallel to each other. The voltage across all components in a parallel circuit is equal but the current is not. The current is shared equally between all of the separate branches of the circuit. The sum of the current measured on each branch of the circuit should be equal to the total current flowing around the circuit. This means that the total amount of current flowing around the circuit is split between each parallel branch of the component. The diagram below shows an example of a parallel circuit:

As each component in a parallel circuit is on a separate loop of the circuit, if one component breaks, the current is still able to travel along the other unbroken branches. The components on the other branches will therefore still be able to work. Let’s return to our previous example of the Christmas tree lights. If the lights were connected in a parallel circuit and one of the bulbs failed, the rest of the lights would stay lit. It would be very easy to then identify and replace the broken bulb. Parallel circuits are used in domestic lighting for the same reason. For example, if a bulb failed in the kitchen, the rest of the lights in the house will remain lit. Series and parallel circuits have different characteristics and this makes them suitable for different applications.

In a series circuit:

• One switch can turn all the components on and off together.
• If one bulb or device breaks, all the other bulbs or devices will stop working.
• The voltage supplied by the cell or mains supply is shared between all the components. The more bulbs added to the series circuit, the dimmer they will become.
• The larger the resistance of any component, the bigger the share of voltage in the circuit.

In a parallel circuit:

• Switches can be placed in different parts of the circuit to switch each bulb on and off individually.
• If one bulb or device breaks, only the bulbs on the same branch will be affected.
• Each branch of the circuit receives the same voltage, so if more bulbs are added to the circuit in parallel their brightness is not affected.

Decorative fairy lights are usually wired in series. This is because every bulb only needs a low voltage. If the voltage from the mains supply is shared out between each bulb, they still get enough energy to produce light. If one of the bulbs is not in its holder properly or breaks, the circuit will no longer be complete and none of the bulbs will light up.

The lights in your homes are wired in parallel. Each bulb can be switched on and off separately and the brightness of the bulbs does not change when other bulbs are on or off. If one bulb breaks or is removed, you can still use the other lights in the house.

### Current and voltage in series and parallel circuits

The current in a circuit is usually measured using a device called an ammeter. The ammeter is placed in a series with the component through which the current passes and therefore becomes part of the circuit. It is able to measure the size of the current running through it.

The ammeter must have a low resistance as, if it doesn’t, it will cause the current to decrease and the value measured would not be accurate. The diagram opposite shows the typical position of an ammeter in relation to the circuit.

To measure the potential difference or voltage across components in a circuit such as cells or lamps, we use a device known as a voltmeter. Voltmeters must be connected in parallel to, or across, the component we are measuring the potential difference across.

The voltmeter, when placed in parallel to a component, will measure the amount of energy that is transferred to each coulomb of charge that passes through it. The diagram opposite shows the typical position of the voltmeter in a circuit where it is placed parallel to the component that it is measuring the potential difference across.

#### Current and voltage in a series circuit

In a series circuit, the current flowing through all components is equal. Therefore, if the current was measured at any point in the circuit, it should always be equal. For example, if a current of 0.4A was measured at the start of the circuit, the current measured at any other point in the circuit should also be equal to 0.4A.

The size of the current is dependent upon the total voltage supplied by the cells or batteries, as well as the number and nature of the components included in the circuit. If more components are added, the current will reduce as each of these has a resistance to the electricity flow.

The voltage in a series circuit is not equal across all components. The voltage is shared equally amongst the components of the circuit as long as their resistances are equal. For example, if a battery in a series circuit produces 6V and we have three components in the circuit, the voltage measured across each component will be 2V. If the resistances of the components are unequal, the voltage measured across the components will differ.

Look at the images of two series circuits above. The one on the left shows the results of a voltmeter being placed in the circuit at different points and we can see that 6 volts is the power from the battery. This is then split among the components so each one has a measurement of 3V. The image on the right shows the same circuit but this time with the results of an ammeter. We can see that the current (measured in amps) is the same throughout the circuit.

### Current and voltage in a parallel circuit

In a parallel circuit, the current is divided up along different branches then combines again when returning to the battery. The current measured before and after the branches should be equal. Each branch of the circuit will have a percentage of the initial current measured. The sum of the current measured on all branches should be equal to the total current measured at the start and end of the circuit.

For example, consider a parallel circuit with two branches where the initial current measured was 0.4A. Each of the two branches has only one bulb. The current will run through both branches and both bulbs equally so the current measured on both branches would be 0.2A, as shown in the diagram above.

The voltage or potential difference (p.d.) across components connected in a parallel circuit is always equal. Each branch will have the exact same p.d. and this value does not change, unlike in a series circuit. For example, the diagram above shows a parallel circuit with two branches. The battery has a p.d. of 6V and each branch also has a p.d. of 6V

### How to measure current

To measure the current flowing through a circuit we use an ammeter. The ammeter is connected in series with the components and provides a measure of the rate at which the charge is flowing through the circuit.

As we have already discussed, electrical charge is measured in coulombs (C). One coulomb is the equivalent of around six million, million, million electrons. This should give you a sense of how tiny electrons really are! One coulomb of charge passing through an object each second is equal to one amp.

To calculate the charge that passes through a wire we use the equation:

Q=I×t
where Q= Charge (in coulombs), I= Current (in amps) and t= Time (in seconds)

You must be able to rearrange this equation to find current, charge or time depending upon the values provided in the exam question.

In order to find current, charge and time we can use a formula triangle as shown in the diagram below. The value you wish to calculate is covered and you look at the two values remaining. If these are shown one on top of the other, then you need to divide the top number by the bottom number. If they are shown side-by-side, then you must multiple the two values.

Example

If a wire has a current of 12A running through it for 8 seconds, calculate the charge.

Here we use our equation of Q=I×t and substitute in the current and time:

Q=I×t
Q=12A×8s
Q=96 coulombs

Example

If the charge is 120C and the time taken was 12 seconds, calculate the current needed. Here we rearrange the equation to give us I = Q  t and substitute in the values:

### Energy transfer

As discussed previously, the energy transferred to the components (in joules) can be calculated using the equation below:

If the charge has not been provided but the current and time has been, the amount of energy transferred can also be calculated using the equation:

Example

Calculate the energy transferred over a period of 45 seconds if the current was 30A and the voltage was 5V.

Energy transferred = 30A x 5V x 45s

Energy transferred = 6,750 joules

### Investigating the relationship between current and voltage

The relationship between voltage and current can be investigated experimentally for a variety of components. The method for such an experiment is outlined as follows:

1. Set up a series circuit containing a battery, ammeter, component being tested, voltmeter placed across the component and a variable resistor.
2. Record the initial current and voltage shown on the ammeter and voltmeter.
3. Change the setting on the variable resistor to alter the current flowing through the circuit and the voltage across the component.
4. Take another reading of the altered current and voltage.
5. Repeat steps 3 and 4 at least five times to collect several measurements of the current and voltage.
6. Repeat steps 2–5 twice and calculate an average voltage for each current.
7. Swap the wires around so that the terminals of the cell have been reversed and repeat steps 2–6.
8. Plot a graph of the current against voltage. This is known as an I-V graph.
9. Repeat the experiment for each component to be tested.

Some components produce characteristic I-V graphs which you must be able to describe, understand and explain.

For a wire or fixed resistor at a constant temperature, the current flowing through is directly proportional to the voltage across it. The typical graph drawn to illustrate this relationship is shown in the diagram below:

When current flows through the metal filament in a lamp, the filament heats up and its resistance increases. This change in resistance means that the current and voltage are no longer directly proportional. As the resistance increases, the current decreases so the graph becomes shallower, as shown in the diagram below of the typical I-V graph for a filament lamp:

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