physics

Series vs Parallel Circuits

Series and parallel circuits differ in how components are connected, so current, voltage and resistance behave differently in each. Learning these rules helps you calculate circuit values and understand why household wiring is usually arranged in parallel.

Visual note, a 3:14 episode with transcript, a mind map, 12 flashcards and a 5 question quiz.

Series vs Parallel Circuits at a glance

Visual note summarising series vs parallel circuits

Listen: Series vs Parallel Circuits

Two hosts talking it through, 3:14. The full transcript is below, so you can read along or skip the audio.

Transcript

AnnaToday we’re comparing series and parallel circuits. Marco, what is the basic difference?

MarcoIt is how the components are connected. In a series circuit, components are connected one after another in one continuous path. In a parallel circuit, they are on separate branches between the same two points. So, in series, charge has one route. In parallel, it has several.

AnnaHow does that change the current and voltage in a series circuit?

MarcoThe current is the same through every component, because charge cannot divide between paths. But the supply voltage is shared. The voltage drop across each resistor depends on its resistance. If two resistors carry the same current, the larger resistance has the larger voltage drop.

AnnaAnd what happens to total resistance when we add resistors in series?

MarcoWe add them directly. The total resistance equals R one plus R two plus R three. Adding another resistor always increases total resistance. With a fixed supply voltage, Ohm’s law, current equals voltage divided by resistance, means the circuit current decreases. Also, the supply voltage equals the sum of all the voltage drops.

AnnaSo what is the matching rule for a parallel circuit?

MarcoThe voltage is the same across every branch, because every branch connects directly across the supply. The total current divides between the branches. A branch with lower resistance carries more current. The total current is the sum of the branch currents.

AnnaPeople often add parallel resistances directly. Why is that wrong?

MarcoDirect addition is for series resistors. For parallel resistors, we add reciprocals. One divided by total resistance equals one divided by R one, plus one divided by R two, plus one divided by R three. For two resistors, total resistance equals R one times R two, divided by R one plus R two. The result is always less than the smallest individual resistance.

AnnaWhat does adding another parallel branch do?

MarcoIt provides another path for current. If the supply voltage stays the same, total current from the supply increases.

AnnaLet’s talk about failures. What happens if a component becomes an open circuit in series?

MarcoThe single path is broken, so current stops everywhere. Every component goes off. That is why one failed bulb can turn off a whole string of series-connected lights.

AnnaAnd in parallel?

MarcoOnly that branch loses current. Other branches can still operate through their separate paths. But a short circuit is different. It creates a very low resistance path, which can cause dangerously large current and make a fuse or circuit breaker disconnect the supply.

AnnaWhy is household wiring mainly parallel?

MarcoAppliances receive the full supply voltage and can be switched independently. If one appliance is turned off or fails open circuit, the others can continue working. Parallel connections are also common in lighting systems and circuits whose branches need to operate independently.

AnnaSo the key warning is not to confuse current sharing in series with current division in parallel, or voltage sharing in series with equal voltage in parallel.

MarcoExactly. One path means the same current. Separate branches mean the same voltage across each branch.

The notes

What a series circuit is

In a series circuit, components are connected one after another in a single continuous path. There is only one route for charge to move through the circuit.

The current is the same through every component because charge cannot divide between different paths. The supply voltage is shared between the components. The voltage across each resistor depends on its resistance, so a larger resistance has a larger voltage drop when the current is the same.

Resistance in series

The total resistance of resistors in series is found by adding their resistances: Rtotal = R1 + R2 + R3. Adding another resistor in series always increases the total resistance.

For a fixed supply voltage, Ohm’s law, I = V ÷ R, shows that increasing total resistance reduces the current in the circuit. The supply voltage is equal to the sum of the voltage drops across all the components.

What a parallel circuit is

In a parallel circuit, components are connected on separate branches between the same two points. This gives charge more than one possible path through the circuit.

The voltage is the same across every branch because each branch is connected directly across the supply. The total current divides between the branches, and the current in each branch depends on the resistance of that branch. A branch with lower resistance carries more current.

Resistance in parallel

For two or more resistors in parallel, the reciprocal formula is 1 ÷ Rtotal = 1 ÷ R1 + 1 ÷ R2 + 1 ÷ R3. For two resistors, this can also be written as Rtotal = (R1 × R2) ÷ (R1 + R2).

The total resistance of parallel resistors is always less than the smallest individual resistance. Adding another parallel branch provides another path for current, so total current from the supply increases when the supply voltage stays the same.

What happens when a component fails

If one component in a simple series circuit fails by becoming an open circuit, the single path is broken. Current stops everywhere in the circuit, so all components go off. This is why one failed bulb can turn off an entire string of series-connected lights.

If one branch in a parallel circuit becomes an open circuit, current stops only in that branch. The other branches can still operate because they have separate paths. However, if a component fails as a short circuit, it creates a very low resistance path, which can cause a dangerously large current and may make a fuse or circuit breaker disconnect the supply.

Uses in practice

Series circuits are used when the same current must pass through components in sequence. Examples include some simple strings of lights, series switches, and voltage dividers. Batteries can also be connected in series to increase the total voltage, provided their ratings and charging requirements are suitable.

Parallel circuits are used in household and building wiring because appliances receive the full supply voltage and can be switched independently. If one appliance is turned off or fails open circuit, other appliances can continue working. Parallel connections are also common in lighting systems and circuits where separate branches need to operate independently.

What to remember

In a series circuit, the current is the same through every component.
In a series circuit, the supply voltage is shared between components.
Series resistance is Rtotal = R1 + R2 + R3.
In a parallel circuit, the voltage is the same across every branch.
In a parallel circuit, total current is the sum of the branch currents.
Parallel resistance follows 1 ÷ Rtotal = 1 ÷ R1 + 1 ÷ R2 + 1 ÷ R3.
A failed open circuit stops all current in a series circuit but usually affects only one branch in a parallel circuit.
Household circuits are mainly parallel so appliances can work independently at the full supply voltage.