Series and Parallel Circuits (GCSE Physics)

Series and Parallel Circuits

What is the Difference Between Series and Parallel Circuits?

There are two main types of circuits:

• Series circuits – in a series circuit, all components are connected in line with each other.
• Parallel circuits – in parallel circuits, the components are connected in separate loops.

Some circuits can have both series and parallel parts.

Series Circuits

There are a few rules and facts about series circuits that we need to remember.

• Current is the same in all parts of the circuit. Current is not ‘used up’ along the circuit, so remains constant. You can calculate the current by dividing the total voltage of the battery or cell by the total resistance in the circuit.
• Total voltage is shared amongst components. The total voltage from the battery / cell is shared between the components – if the battery or cell provides 5V of energy, and there are two lamps (with equal resistance), each lamp will get 2.5V.
• Total resistance is the sum of the resistances of all components. Current needs to be the same everywhere, so the higher the resistance of an individual component, the greater its share of the voltage (so that current, which is voltage / resistance, stays equal). Therefore if you add an extra lamp to a series circuit, the total resistance increases and hence the current decreases. All lamps become dimmer. We can use the following equation to work out the total resistance in a series circuit:

Where:

• Resistance, R, in ohms, Ω

• Cell voltages sum together. If there are two cells or batteries, then the voltage from both add up together to give the total circuit voltage.
• A break in one component ruins the whole circuit. There is only one route for charge, so if one lamp in a series circuit is broken, all lamps will stop working. Christmas lights are often sometimes in series circuits, because each bulb only needs a small voltage, so it is better to share the voltage in series. However, this means that if one light breaks then they all break.

Parallel Circuits

The voltage is the same for all components. In series circuits the voltage was shared between the components (in proportion of their resistance). In parallel circuits, every single component gets the full, maximum voltage. Therefore bulbs in parallel will have the same brightness (assuming equal resistance). This means more components may be added in parallel without needing extra voltage.

• The current is split between the branches of the circuit. The sum of the currents of all branches is equal to the total current that flows from the cell / battery. In other words, the total current through the whole circuit is the sum of the currents through the separate components.

• A break in one component does not ruin the whole circuit. There is more than one route for charge, so if one lamp in a parallel circuit is broken, only the lamps in the broken branch are affected. Lighting in houses is often connected in parallel because it means that we can control different branches of the circuit (representing different rooms) using different switches.

• Total resistance is worked out using the reciprocal of the resistances of each branch. If there are 3 branches to the circuit (R1 – R3), then 1 / Total Resistance = 1 / R1 + 1 / R2 + 1 / R3. This means that the total resistance of two resistors is less than the resistance of the smallest individual resistor.

Where:

• Resistance, R, in ohms, Ω

Resistors

• Resistors in series increase resistance. In a series circuit, adding resistors will increase resistance. The current is the same in every single component in the circuit, so the more resistors we add, the harder it is for current to flow. This means that the overall resistance has increased in a series circuit.
  • The more resistors added, the harder it is for current to flow.
• Resistors in parallel decrease resistance. In a parallel circuit, adding resistors will decrease the resistance. The potential difference is the same in every single component in the circuit. The more resistors we add in parallel, the more ‘pathways’ the current has to go through, so it is easier for current to flow through the circuit. This means that the overall resistance has decreased in the circuit. The more resistors added, the easier it is for current to flow through many pathways.
  • The more resistors added, the easier it is for current to flow through many pathways.

Calculating Resistance in Series

For exams, we need to be able to calculate the combined resistance, also called the equivalent resistance, of resistors.

Question: In the diagram below, there are two resistors in series. R1 has a value of 20 ohms, whilst R2 has a resistance of 10 ohms. Find the equivalent resistance of the two resistors.

We need to remember that the equivalent resistance simply means the total of the resistors in the circuit.

R total = R1 + R2
R total = 20 + 10
R total = 30 Ohms

Summary Comparison: Series vs. Parallel Circuits

Investigating Resistance in Experiments

Experiments with Series Circuits

For exams, we need to design and use dc series circuits. We can use these circuits to investigate resistors.

Method:

1. Set up circuit. We have to set up a circuit with a cell (battery), an ammeter and a resistor in series.
2. Check the circuit. Make sure that the circuit is complete and working.
3. Measure PD. Record the potential difference of the cell, in volts.
4. Measure current. Measure the current in the circuit using an ammeter, recording the value in amps.
5. Calculate resistance. Calculate the resistance in the circuit, by rearranging V = IR. Record the value for resistance in ohms.
6. Change quantity of resistors. Add another resistor to the circuit and then repeat steps 2-5.
7. Fill in a table. The results table should look something like this:
   
8. Plot a graph. Using the results, we can make a graph of ‘quantity of resistors’ (x axis) against ‘total resistance’ (y axis).

Experiments with Parallel Circuits

You can also investigate resistors in parallel. The experimental process is largely the same.

In exams, this is an example of application questions. You should have learnt the experimental set up for series, so they want to see you apply your same knowledge to a less familiar scenario (in parallel)

Short Circuits

Current likes to take the easiest path with the least resistance. In this diagram, if switches P and Q are closed in this circuit, then neither lamps will be lit. The current prefers to pass through plain wire than the lamps, because plain wire has a lower resistance. Therefore a short circuit is formed.

When the switches are open, the current is forced to go through the bulb, and so the bulb lights up.

For this kind of circuit, there is no parallel split in current. If the plain wire path is available, then all of the current will go down that pathway.