Series and parallel resistors, without the headache

Two resistors, two ways to connect them. One way the current has to go through both. The other way it can pick. The numbers change a lot, and so does which resistor gets hot.

Play with it first. Add resistors, switch between series and parallel, and watch the current column.

Series: one path

In series the resistors sit one after the other, so the current has only one way to go. That means:

• The current is the same in every resistor.
• The resistances add up. 100 + 220 + 330 = 650 Ω.
• The voltage splits. The biggest resistor gets the biggest share of the voltage.

Example: those three on 9 V. 9 ÷ 650 = 13.8 mA through all of them. The 330 Ω one gets about 4.6 V, the 100 Ω one about 1.4 V. Check it in the table above.

Parallel: several paths

In parallel every resistor is connected straight across the supply. The current splits between them:

• Every resistor gets the full voltage.
• The currents add up. Each branch takes what Ohm's law gives it.
• The total is always smaller than the smallest resistor. More paths means less resistance overall.

The formula is 1 ÷ total = 1 ÷ R1 + 1 ÷ R2 + 1 ÷ R3. Don't worry about it, the calculator does it. The one shortcut worth remembering: two equal resistors in parallel give half. Two 220 Ω make 110 Ω.

Now look at the heat

Switch the same three resistors to parallel on 9 V. The total drops to about 57 Ω and the circuit pulls around 158 mA. The 100 Ω resistor alone takes 90 mA and turns about 0.8 W into heat. A normal 1/4 W resistor would get far too hot.

Same parts, same battery, and one of them is now cooking. That's why you always check power, not just resistance. Power = voltage × current, the table does it for every resistor.

When to use which

• Series when you want to drop voltage or limit current, like the resistor in front of an LED. Also to build a value you don't have: 1 kΩ + 220 Ω = 1.22 kΩ.
• Parallel to get a smaller value you don't have, or to share heat. Two 220 Ω in parallel give 110 Ω, and each one only carries half the power.
• Parallel is also how the things in your house are connected. Every socket gets the full voltage, and turning one lamp off doesn't turn off the others.

Mixed circuits

Real circuits mix both. Solve them in pieces: combine the parallel groups into one value, then add up what's left in series. Then work backwards for the currents. It looks scary, but it's the same two rules over and over.

If Ohm's law itself is still shaky, start with Ohm's law without the boring part. Two resistors in series are also a voltage divider, which is the next useful trick.