Series vs parallel circuits

Every multi-component circuit is built from two fundamental wiring patterns: series and parallel. They behave in opposite ways, and knowing how voltage, current and resistance combine in each lets you analyse almost any network by breaking it into these building blocks.

Series: one path for everyone

In a series circuit, components are joined end to end in a single loop. There is only one route for charge to take, which leads to one defining rule: the current is the same through every component.

Because the parts share one current but each has its own resistance, the supply voltage is divided between them. The individual voltage drops always add back up to the supply, an idea formalised as Kirchhoff’s voltage law. Series resistances simply add:

R_total = R1 + R2 + R3 + …

So two 100 Ω resistors in series make 200 Ω. Adding more components in series always raises the total resistance, which lowers the current.

Worked example. A 12 V supply drives two 100 Ω resistors in series. The total resistance is 200 Ω, so the current is I = 12 / 200 = 0.06 A. Each resistor drops V = I x R = 0.06 x 100 = 6 V, and 6 + 6 = 12 V, matching the supply.

This is also why some older string lights all go dark when a single bulb fails: the bulbs are in series, so one broken filament opens the only path.

Parallel: shared voltage, split current

In a parallel circuit, components connect across the same two nodes. This gives the opposite defining rule: every branch has the same voltage across it, equal to the supply.

Because each branch sees the full voltage but has its own resistance, the current splits between branches, with lower-resistance branches drawing more. The branch currents add up to the total, which is Kirchhoff’s current law. Parallel resistances combine by reciprocals:

1 / R_total = 1/R1 + 1/R2 + …

A handy consequence: the total is always less than the smallest branch. Two equal resistors in parallel give half the value.

Worked example. A 12 V supply drives two 100 Ω resistors in parallel. The total resistance is 100 / 2 = 50 Ω, so the supply current is I = 12 / 50 = 0.24 A. Each branch carries 12 / 100 = 0.12 A, and the two branches add back to 0.24 A.

Side-by-side summary

Why houses are wired in parallel

Mains outlets, lights and appliances in a building are all wired in parallel, and the table above explains why. Parallel wiring delivers the full mains voltage to every device, so a 230 V kettle and a 230 V lamp both get exactly what they need. Just as important, each device can be switched on or off independently without breaking the path to the others.

If a home were wired in series, the supply voltage would be split among everything plugged in, so each appliance would receive only a fraction of the voltage, and that share would shift every time another device turned on or off. Worse, switching one appliance off would open the loop and kill power to everything. Parallel wiring avoids all of this, at the cost of needing protective devices (fuses or breakers) because each branch can draw its own current and the total can become large.

Analysing real circuits

Most practical circuits are neither purely series nor purely parallel but a mix. The strategy is to collapse the network step by step: combine obvious series groups into single equivalent resistors, combine parallel groups into their equivalents, and repeat until you have one total resistance. From there, Ohm’s law gives the overall current, and you work back outward to find the voltage and current in each part. With the two combination rules and Kirchhoff’s laws in hand, even a tangled-looking network becomes a series of small, manageable steps.