Parallel Circuits

A parallel circuit consists of multiple branches. This means that the electrons have multiple paths to flow.

*Remember, conventional current flows from the positive side (the longer side of the cell) to the negative side in a complete loop.

The electrons all leave the cell and split at the first junction. Some will flow through the red path, and some through the blue. The current splits. At the junction on the right-hand side, the electrons meet up again and the current combines.

We can see this in the diagram below, where of current leaving the cell splits at the first junction. The amount of current in each branch depends on the resistance of the components in that path -> higher resistance = lower current. In this diagram, the bulbs in each path are identical, so the current splits exactly in half, takes the top path and flows through the bottom path. When the two paths meet again at the junction on the right-hand side the currents add together to give again, the original current from the cell.

We can write this rule in equation form as:

If we had a third branch we could add it as and so on. Within each branch, the current will be the same before and after the component - just as in a series circuit, as the electrons only have one path in this branch.

One of the advantages of parallel circuits is that if a component breaks in one branch, the whole circuit will not break as the electrons have got other pathways to flow through.

Example: We can use this rule to find the missing ammeter reading in the circuit below:

The current into and out of the cell is the same, so . The current in the first branch is , so and we need to work out .

In a parallel circuit, the potential difference across each branch is the same. This is because potential difference—defined as the energy transferred per coulomb of charge, —remains constant regardless of the path taken, as each coulomb of charge receives the same amount of energy from the power supply.

We can see this below, the cell provides . Each coulomb of charge leaves the cell with of energy, and we learned when studying series circuits that they must return to the cell with zero energy. If a coulomb of charge (electrons) takes the top branch, they have only one component to pass through, so they transfer all their energy across that component. The potential difference (difference in energy per coulomb of charge between two points in a circuit) is . If they take the middle path, they still have only one component to pass through, so they transfer all their energy through that component; the same goes for the bottom path. Therefore, the pd across each branch in a parallel circuit is the same.

We can write this in an equation as:

If there are two or more components along a branch, they will share the potential difference of the branch, just like in a series circuit.

Example: We can use this rule to work out what value the voltmeters at A and B in the circuit show:

We know that the potential difference across each branch will be the same as that across the cell. As if each coulomb of charge gains and must return to the cell with zero energy they must transfer all of their energy across the branch.

In the bottom branch, the resistor is the only component, so all energy per coulomb of charge is transferred across this one component. Therefore, the potential difference at B will be .

In the top branch, there are two components, a resistor and a cell. Each coulomb of charge must transfer six joules of energy across the entire branch. If they have two components to get through, they will lose some of their energy across the first component and some across the second. If the potential difference across the bulb is , the potential difference across the resistor will be , so voltmeter A reads .