GCSE Science/Parallel and series circuits
You will have already studied series and parallel circuits before, so you should be familiar with what a series and parallel circuit is and their basic properties. But in this module we will be looking at them in a little more detail. We will apply Ohm’s law to see how we can work out the resistance of a whole circuit that is made up of a large number of components. Before we begin you might want to try some revision questions.
Resistors in Series Circuits
As we know, in a series circuit the current in all parts of the circuit is the same and the current has a one way system. The current depends on the applied voltage and the number of and nature of other components in the circuit.
Consider two resistors in a series circuit with a battery. As you might expect the total resistance in this circuit is higher than the resistance of each resistor, because the battery has to ‘push’ the charge through both resistors one after the other. So the total potential difference of the supply is ‘shared’ between the two resistors.
Think about what is happening to the current as it flows around the circuit. There are no branches, nowhere for the electric current to escape to, so obviously the same current must flow through both resistors. Let’s call this current I.
The total resistance for the whole circuit is very simple. It’s just R1 plus R2.
Formula for resistance of two resistors in series
RTotal = R1 + R2
The total resistance in a series circuit is the sum of the resistances of all the components.
Using this formula we can calculate the voltage across each resistor. But it could depend on how many resistors there are.
Example: Calculating voltages in a series circuit
| Question | |||
|---|---|---|---|
| Suppose R1 = 1Ω and R2= 4Ω. If the battery supplies 2.5 volts, what is the voltage across each resistor. | |||
| Answer | |||
| 1st step | First use the total resistance of the circuit to work out how much current is flowing through the circuit.
Work out the total resistance | ||
| identify formula: | RTotal = R1 + R2 | ||
| insert numbers and units | RTotal = 1Ω + 4Ω = 5Ω | ||
| 2nd step | Use Ohms’s law to calculate the current in the circuit. Decide which resistance to use. | ||
| identify formula (using the triangle): | I = V / R (Ohms’s law) | ||
| decide which resistance to use: | Use RTotal; so formula becomes I = V / RTotal | ||
| insert numbers and units | I amps = 2.5V / 5Ω = 0.5A | ||
| Now we know how much current is flowing through both resistors, we can work out the voltage across each resistor. | |||
| 3rd step | Use Ohm’s law to calculate the voltage across each resistor: | ||
| identify formula (using the triangle): | V = I x R | ||
| insert numbers for resistor 1: | V1 volts = 0.5A x 1Ω = 0.5 volts | ||
| insert numbers for resistor 2: | V2 volts = 0.5A x 4Ω = 2.0 volts | ||
Practice questions
Resistors in Parallel Circuits
Parallel circuits are a bit more complicated than series circuits, because they contain a branch – the electric current will take more than one route. Look at the diagram. At point X the current splits into two paths, and flows through both resistor R1 and resistor R2. It may not split in equal amounts. When several (two or more) components are connected in parallel branches, the voltage (potential difference) across each parallel branch is the same. And this is the same as the voltage across the battery.
The current through each component is the same as if it were the only component present. So the total current flowing through the battery is the sum of the currents flowing through each branch. Here is the formula for the currents flowing through a parallel circuit.
IMain = I1 + I2
Because the voltage is the same for all branches, the branch with the lowest resistance has the highest current flowing through it. Because there are more paths for the charge to flow along, the total resistance is less than either of the two paths on their own. And therefore (with the same battery) the current is bigger.
To find out the resistance of the whole circuit, we can’t just add together the resistors as we did in the series circuit, we have to apply Ohm’s law to each branch of the circuit.
Imagine we replaced the resistors with bulbs. You should now be able to answer the following questions from your previous knowledge.
If you answered the above questions correctly you should find this next section easy!
Example: Calculating the resistance of several resistors in parallel
It’s best to break the process down into a number of simple steps. Some books may give you a formula to use, but you shouldn’t use any formula without understanding where it comes from (otherwise you are likely to remember it incorrectly or apply it inappropriately). By using a simple step by step method instead you can get a feel for why it works, and you will be far less likely to make a mistake in the exam.
- 1st step
- Consider each branch on its own, as if the other branch didn’t exist, and use Ohm's law to work out the current flowing through each branch.
- 2nd step
- Add the currents together to find out the total amount of current flowing through the whole circuit.
- 3rd step
- Apply Ohm’s law again to work out the total resistance of the circuit.
Example
Suppose V=2V R1 = 1Ω and R2= 1Ω.
| 1. | Applying Ohm‘s law to the branch containing R1 gives |
| 1=I1 = V / R1 = 2V / 1Ω = 2A | |
| 2. | Applying Ohm’s law to the branch containing R2 gives |
| I2 = V / R2 = 2V / 1Ω = 2A | |
| Total current = I1 + I2 = 4A | |
| 3. | Applying Ohm’s law again, to the whole circuit. |
| 1=RTotal = V / Itotal = 2V / 4A =0.5Ω |
Notice that the resistance of the whole circuit is lower than the resistance of either branch!
Practice questions
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Summary
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