Series and parallel circuits

In a nutshell

The total current, potential difference and resistance in a series circuit is different to that of a parallel circuit. The current in series is the same around the circuit, but is split at branches in parallel. The potential difference is split across components in series, but each branch in parallel is has the same potential difference. And resistance in series is just the sum of the resistors, but in parallel is less than the lowest resistance branch.

Series circuits

Series circuits are circuits where components are placed one after another and they form a large loop. 

Current in a series circuit

Current is the flow of electrical charge. As all of the components are connected in a loop, the charge has to flow through all of the components. 

In a series circuit, there is only one path for the current to take, so the amount of current flowing before the component must be the same as the current flowing after the component. Therefore, current in a series circuit is the same everywhere.

Potential difference in a series circuit

Potential difference is the difference in potential between two points in a circuit. The power supply provides the electric energy to the charge carriers and the charge carriers transfer the energy to the components around the circuit. 

The electric potential of the charge carriers must be used up around the circuit, across all of the components. So, in a series circuit, the potential difference is shared across all of the components in a series circuit. 

Resistors in a series circuit

Resistance is the measure of how difficult it is for current to flow. In order to get current to flow through an electrical component it takes electrical potential. The higher the resistance of the electrical component, the more electrical potential it takes. 

When current flows through a single resistor, it will use all of its electrical potential to travel through it, as all the electrical potential has to be used up before returning to the power supply.

This means that as more resistors are added in series, the higher the combined resistance of the circuit. So when resistors are added in series, the values of their resistances are added together. $$R_T=R_1+R_2+R_3+...$$

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The total resistance of this circuit is: $$200 \, \Omega+400 \, \Omega=600 \, \Omega$$​​	​The total resistance of this circuit is: $$20 \, \Omega+60 \, \Omega=80 \, \Omega$$

Parallel circuits

Parallel circuits are circuits where there are branches and electrical components run parallel to one another.

Current in a parallel circuit

Parallel circuits have branches, which means that electrical charge can flow along different paths. Electricity takes the path of least resistance so more current will flow along the path which has the least total resistance. 

So, in a parallel circuit, current is split across the branches, depending on the total resistance of the branches. 

Potential difference in a parallel circuit

When the power supply gives electric potential to the charge carriers, each charge carrier takes a certain amount of energy. In a parallel circuit, when the charge carriers come across a branch, they can only travel down one path. 

The charge carriers must use up all of their energy before getting back to the power supply. This means that the electric potential supplied at the power supply will get used up along each branch of the parallel circuit. This means that the potential difference along the branches of a parallel circuit is the same. 

Resistors in a parallel circuit

In a parallel circuit, there are now different pathways electrical charges can take. If there is a path of very high resistance and a path of very low resistance, a lot of the electric current will flow down the path of low resistance. 

This means a lot of the current will not flow through the high resistance. So, when adding resistors in parallel, the total resistance of the circuit will always be less than the lowest branches total resistance. 

The total resistance of this circuit will be less than the resistance of the lowest branch, so  $$R_T<200 \, \Omega$$.​	The total resistance of this circuit will be less than the resistance of the lowest branch, so $$R_T<20 \, \Omega$$.​

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