Series and Parallel Circuits

Compare series and parallel circuits — how resistance, voltage, and current behave differently in each arrangement.

Two Ways to Connect Components

In a series circuit components are connected in a single loop. In a parallel circuit components are connected across the same two nodes.

Series Circuit

Quantity	Rule
Current	$I$ is the same everywhere
Voltage	$U_{total} = U_1 + U_2 + \ldots$
Resistance	$R_{total} = R_1 + R_2 + \ldots$

Warning If one component in a series circuit breaks, the entire circuit stops working (like old Christmas lights).

Parallel Circuit

Quantity	Rule
Voltage	$U$ is the same across each branch
Current	$I_{total} = I_1 + I_2 + \ldots$
Resistance	$\dfrac{1}{R_{total}} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \ldots$

Note Parallel wiring is used in homes — each device gets the full mains voltage and operates independently.

Comparing the Two

Feature	Series	Parallel
Current through each component	Same	Different (splits)
Voltage across each component	Splits	Same
Total resistance	Increases	Decreases
Failure of one component	All stop	Others continue

1
Identify the circuit type
Is it series (one loop) or parallel (multiple branches)?
2
Apply the correct rules
Series: R adds; Parallel: 1/R adds.
3
Find total R, then I or V
Use Ohm's law: U = IR.

Two resistors R₁ = 4 Ω and R₂ = 6 Ω are connected in series to a 20 V battery. Find total resistance and current.

$R_{total} = 4 + 6 = 10\ \Omega \qquad I = \frac{20}{10} = 2\ \text{A}$

The same resistors are now in parallel with a 12 V battery. Find total resistance and total current.

$\frac{1}{R_{total}} = \frac{1}{4} + \frac{1}{6} = \frac{5}{12} \implies R_{total} = 2.4\ \Omega \qquad I = \frac{12}{2.4} = 5\ \text{A}$

Real world: car lights (parallel wiring)

The headlights, brake lights, and indicators on a car are connected in parallel. Each light receives the full 12 V battery voltage, so the others keep working if one bulb blows. This is why a car does not go dark when one indicator fails.

Real world: home electrical sockets (parallel)

Every socket in a house is wired in parallel across the 230 V mains supply. Each appliance receives 230 V regardless of how many others are plugged in. The total current drawn increases as more appliances are added, which is why a main fuse can trip if too many high-power devices run at once.

Real world: old-fashioned Christmas lights (series)

Traditional series Christmas lights fail completely when one bulb blows because the circuit is broken at that point. Modern lights are wired in parallel so only the faulty bulb goes out. Understanding series vs parallel wiring directly explains this familiar experience.

Tip If you need to know which type of circuit you have: measure voltage across each component. Equal voltage in every branch → parallel. Voltages that add to the supply → series.

Practice Problems

Three 6 Ω resistors in series. What is the total resistance?

Show answer

R = 6 + 6 + 6 = 18 Ω.

Two 8 Ω resistors in parallel. What is the total resistance?

Show answer

1/R = 1/8 + 1/8 = 2/8 → R = 4 Ω.

A series circuit has R₁ = 3 Ω, R₂ = 7 Ω, and runs on 10 V. What current flows?

Show answer

R_total = 10 Ω; I = 10/10 = 1 A.