# Series and Parallel Circuits

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## Series and Parallel Circuits

Components can either be connected in series or parallel. The type of circuit can have an effect on the current, potential difference and resistance of the circuit.

## Series Circuits

In a series circuit, circuit components are connected in a single loop, one after another.

The same flow of charge passes through each circuit component and so the current is the same in every component:

$\textcolor{aa57ff}{\text{I}_{\text{total}}=\text{I}_1=\text{I}_2=\text{I}_3=\text{...}}$

The battery or cell provides the supply of potential difference to the circuit.  The potential difference is shared between the other components. So the total potential difference is equal to the potential difference of the battery:

$\textcolor{aa57ff}{\text{V}_{\text{s}}=\text{V}_1+\text{V}_2+\text{V}_3+\text{...}}$

$\textcolor{aa57ff}{\text{R}_{\text{total}}=\text{R}_1+\text{R}_2+\text{R}_3+\text{...}}$

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## Parallel Circuits

In parallel circuits, components are connected in separate loops

Each charge can only flow through one of the loops and so current is shared between loops. So the supply current in the loop with battery is equal to the sum of the current in the other loops:

$\textcolor{f21cc2}{\text{I}_s=\text{I}_1+\text{I}_2+\text{I}_3+\text{...}}$

The potential difference is the same in every loop

$\textcolor{f21cc2}{\text{V}_1=\text{V}_2=\text{V}_3}$

When resistors are connected in parallel, the supply current is shared between the resistors and so the overall resistance is reduced as the electrical charges may take many paths.

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## Example: Series and Parallel Circuit Rules

A student builds a circuit containing a battery and three resistors named $\text{R}1$, $\text{R}2$ and $\text{R}3$. A diagram showing their circuit is shown on the right.

a) Calculate the current at the arrow marked X on the circuit diagram.

[2 marks]

b) What is the potential difference across resistor $\text{R}1$?

[2 marks]

c) Suggest possible values for the potential difference across resistors $\text{R}2$ and $\text{R}3$. Explain your answer.

[2 marks]

a) In parallel, current is shared between loops so:

$\bold{\text{I}_{\text{s}}=\text{I}_1+\text{I}_2}$.

Rearrange for I2 :

$\text{I}_2=\text{I}_{\text{s}}-\text{I}_1=\textcolor{10a6f3}{6\text{ A}}-\textcolor{aa57ff}{3\text{ A}}=\bold{3\text{ A}}$

b) $\bold{\text{R}=\dfrac{\text{V}}{\text{I}}}$

Rearrange to find V:

$\text{V}=\text{IR}=\textcolor{10a6f3}{6\text{ A}}\times \textcolor{00bfa8}{1 \, \Omega}=\bold{6\text{ V}}$

c) $R2$ and $R3$ have the same resistance so potential difference must be equal.

$\text{V}_1 = \text{V}_2=\text{V}_3=6\text{ V}$

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## Series and Parallel Circuits Example Questions

In a series circuit, circuit components are connected in a single loop whereas in a parallel circuit, components are connected in multiple, separate loops

Gold Standard Education

$\bold{5\text{ A}}$

In series, all components receive the same current.

Gold Standard Education

$\text{R}_{\text{t}}=\text{R}_1+\text{R}_2=3 \Omega+3 \Omega=\bold{6 \Omega}$

Gold Standard Education

The parallel circuit has the least overall resistance. This is because in series, each charge carrier must flow through each resistor and so the resistances add up. In parallel, the charge carriers have multiple possible paths and so resistance is less.

Gold Standard Education

$\bold{\text{I}_{\text{s}}=\text{I}_1+\text{I}_2+\text{I}_3}$ (current is shared between the lamps)

Rearrange for I3

$\text{I}_3=\text{I}_{\text{s}}-\text{I}_1-\text{I}_2=20\text{ A}-5\text{ A}-7\text{ A}=\bold{8\text{ A}}$