Physics

2.6 - Parallel Circuits

7 min

What a parallel circuit is

P.d. and current in parallel

Resistance in parallel

note 1 of 3

Parallel circuits and independence

In a parallel circuit, each component sits on its own loop, or branch, connected separately to the supply.

Components work independently

Because the branches are separate, components work independently - if one is disconnected, the others keep working.
This is why parallel circuits are used in cars and house lighting, where lamps and appliances must be switched on and off separately.

A battery with three lamps, each on its own branch across it, labelled independent loops, and after an arrow the same circuit with the middle branch cut and greyed, labelled removed and keeps working.

Mixed circuits

When components are on the same branch in a mixed circuit, the series-circuit rules apply to that branch.

note 2 of 3

Potential difference and current rules

Potential difference is the same across every branch

Each branch gets the full supply potential difference, so the p.d. is the same across all branches: $V_{1} = V_{2} = V_{3} = \dots$
Because each charge travels down only one branch, it transfers all its energy to the components on that branch.
Identical bulbs connected in parallel are therefore all equally bright.

A battery labelled V1 feeding two branches, each with a lamp and a voltmeter across it labelled V2 and V3, beside a box listing each as 5 V and V1 = V2 = V3. — V1 is the supply p.d., V2 and V3 are the branch p.d.s.

The branch currents add up to the total current

The total current equals the sum of the currents in the separate branches: $I_{total} = I_{1} + I_{2} + \dots$
At any junction, the total current going in equals the total current coming out, because charge is conserved.

Current in a single branch

The current in a branch is $I = \frac{V}{R}$ , where $V$ is the supply p.d. and $R$ is that branch's resistance.
The branch with the lowest resistance carries the largest current.
Changing the resistance of one branch only affects the current in its own branch; the other branches are unchanged.

A battery with an ammeter labelled I total, and two branches each with an ammeter and lamp labelled I1 and I2, beside a box reading 5 A = 3 A + 2 A.

note 3 of 3

Why adding a resistor in parallel lowers resistance

The total resistance of a parallel circuit is always less than the resistance of any individual branch.
Adding another resistor in parallel lowers the total resistance further.

The reasoning

Every branch has the full source p.d. across it.
Adding another branch gives the current an extra path, so the current in the existing branches stays the same while new current is drawn.
This increases the total current drawn from the supply.
Since $R = \frac{V}{I}$ and $V$ is constant, an increase in total current means total resistance decreases.

A one-resistor loop labelled same total p.d., an arrow labelled branch added, then the same battery with a second resistor branch, labelled higher total current, plus boxes V = IR and R = V/I.

key terms

TermDefinition

Parallel circuitA circuit where the components are connected on separate branches, so each one can work independently of the others. Components connected across each other like this are said to be in parallel.

BranchA separate loop in a parallel circuit that provides an independent path for current.

end of notes

Key points to remember

Parallel circuits and independence

In a parallel circuit, each component sits on its own loop, or branch, connected separately to the supply.

Components work independently

Because the branches are separate, components work independently - if one is disconnected, the others keep working.

This is why parallel circuits are used in cars and house lighting, where lamps and appliances must be switched on and off separately.

Potential difference and current rules

Potential difference is the same across every branch

Each branch gets the full supply potential difference, so the p.d. is the same across all branches:

V_{1} = V_{2} = V_{3} = \dots

Because each charge travels down only one branch, it transfers all its energy to the components on that branch.

Identical bulbs connected in parallel are therefore all equally bright.

Why adding a resistor in parallel lowers resistance

The total resistance of a parallel circuit is always less than the resistance of any individual branch.

Adding another resistor in parallel lowers the total resistance further.

The reasoning

Every branch has the full source p.d. across it.

Adding another branch gives the current an extra path, so the current in the existing branches stays the same while new current is drawn.

This increases the total current drawn from the supply.

Since

R = \frac{V}{I}

and

V

is constant, an increase in total current means total resistance decreases.