If components in a circuit aren’t connected consecutively and are on different branches of the wire they are said to be connected in parallel. For example:
One of the benefits of a parallel circuit is that if one component breaks or is disconnected, components on other branches will continue to work. This is different to components connected in series.
IMPORTANT NOTE: This post deals with purely parallel circuits. It is possible to have a combination of components in series and parallel within the same circuit.
Current in a Parallel Circuit
The current is distributed between the components. The current through each component may differ, but the total current is equal to the sum of the individual currents (Kirchhoff’s first law):
Where ITotal is the total current of the circuit, I1 is the current flowing through the first component, I2 is the current flowing through the second component and so on. The currents flowing through additional components connected in parallel can be added as required. For example if there was a third component I3 would be added.
Potential Difference in a Parallel Circuit
Kirchhoff’s second law states: In a closed circuit loop the sum of the electromotive forces is equal to the sum of the potential differences. In a parallel circuit the components on separate branches can each form their own closed loop with the source (usually a cell).
Therefore, the potential differences of components connected in parallel are equal to the electromotive force and also each other:
Where V1 is the potential difference across the first component, V2 is the potential difference across the second component and so on.
Resistance in a Parallel Circuit
As new components are added in parallel the current has to be split further. This means that the total resistance of a circuit decreases as more components are added.
The total resistance of a parallel circuit can be calculated using the following equation:
Where RTotal is the total resistance, R1 is the resistance of the first component, R2 is the resistance of the second component and so on. The resistance of as many components as required can be added.
Worked Examples
Example 1
The cell in the circuit below is supplying a current of 5A. Calculate the current flowing through the bulb and state the potential difference across it.
Example 2
Calculate the total resistance of the circuit below.
Example 3
Calculate the current flowing through resistor 2 in the circuit below. The total resistance of the circuit is 10Ω.
This question requires knowledge of Ohm’s law.
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