Resistors in series and in parallel

Most circuits have more than one resistor, and the way they are connected changes everything. There are two basic ways: in series, one after another, so the current has only one path, and in parallel, side by side, so the current can split. This page uses Ohm's law and power, so read those first if you haven't.

Try the tool before reading on. Add resistors, switch between series and parallel, and watch the current column and the heat column.

Series

In series, the same current flows through every resistor, because there is nowhere else for it to go. The total resistance is simply the sum of the resistors: 100 Ω, 220 Ω and 330 Ω in series make 650 Ω.

The supply voltage is shared between the resistors, in proportion to their values. With those three resistors on 9 V, the current is 9 ÷ 650, about 13.8 mA, and each resistor gets current × resistance: about 1.4 V across the 100 Ω, 3 V across the 220 Ω and 4.6 V across the 330 Ω. Together they add up to the 9 V of the supply.

Parallel

In parallel, each resistor is connected directly across the supply, so each one gets the full supply voltage. Each resistor then takes its own current, worked out with Ohm's law, and the total current from the supply is the sum of those currents.

Because there are more paths, the total resistance is lower than the smallest resistor on its own. For two equal resistors it is exactly half: two 220 Ω in parallel make 110 Ω. For other combinations the formula is 1 ÷ total = 1 ÷ R1 + 1 ÷ R2 + 1 ÷ R3, which the tool calculates for you.

The same parts can overheat

Switch the three resistors to parallel on 9 V. The total resistance drops to about 57 Ω and the supply delivers about 158 mA. The 100 Ω resistor alone takes 90 mA and turns about 0.81 W into heat, far more than a common 1/4 W resistor can handle. In series, the same three resistors stayed cool. This is why you always calculate power for each resistor, as described on the power page.

When each one is used

• Series connections are used to limit current, as with the resistor in front of an LED, and to build a value you don't have: 1 kΩ plus 220 Ω gives 1.22 kΩ.
• Parallel connections are used to get a lower value than you have, or to share heat. Two 220 Ω resistors in parallel give 110 Ω, and each one only carries half of the total power.
• The sockets in a house are connected in parallel. Each one gets the full voltage, and switching off one lamp doesn't affect the others.

Circuits that mix both

Real circuits often combine the two. Solve them in pieces: replace each parallel group with its total value, then add up what is left in series. Once you know the total current, work back through the pieces to find each resistor's current and voltage.

Two resistors in series have one more use that gets its own page: the point between them sits at a predictable fraction of the supply voltage. That is the voltage divider.