Resistors in parallel

Parallel means side by side

In a parallel circuit, each resistor connects across the same two points, called junctions or nodes. On a schematic it looks like the rungs of a ladder: one rail on top, one on the bottom, and each resistor is a rung between them.

When the current reaches the first junction, it splits. Some goes through one branch, some through the other, and the streams join again at the second junction before heading back to the battery.

More lanes, more flow

Think of a checkout line. With one register open, everyone waits in one queue. Open a second register and more people get through each minute, even if the new cashier is slow. A second path never makes the total flow smaller; it only adds to it.

That's why adding a resistor in parallel lowers the total resistance. Each branch is one more lane for the current.

Working it out: two 200 Ω resistors on 9 V

The rule for parallel resistors is 1/R total = 1/R1 + 1/R2 + .... For two equal resistors it's even simpler: divide one resistor by how many there are.

• Two 200 Ω resistors: 200 Ω ÷ 2 = 100 Ω. Together they act like one 100 Ω resistor, half of either one.
• In parallel, each branch gets the full battery voltage. On a 9 V battery, each resistor has 9 V across it.
• Current in each branch (Ohm's law): 9 V ÷ 200 Ω = 0.045 A = 45 mA.
• Add up the branches: 45 mA + 45 mA = 90 mA. Check with the total: 9 V ÷ 100 Ω = 90 mA.

So the battery supplies double the current of one resistor alone. That "double" is true for two equal branches; with unequal resistors, the branch with less resistance carries more current.

Always less than the smallest

Add a third branch, say 100 Ω, beside the two 200 Ω resistors: 1/R = 1/200 + 1/100 + 1/200 = 1/50, so the total is 50 Ω. That's less than 100 Ω, the smallest resistor. In parallel, the total resistance is always less than the smallest branch, because every branch adds another path.

Try it yourself

With two equal resistors from a kit, a battery and a multimeter: measure one resistor's resistance, then twist both leads together side by side and measure again. The reading should be about half. If you have a resistance calculator app, try a 1,000 Ω and a 10 Ω in parallel and notice the total is just under 10 Ω.

Good to know

• The rule is 1/R total = 1/R1 + 1/R2 + ...; for equal resistors, the total is one resistor's value divided by the number of resistors.
• Every branch of a parallel circuit has the full source voltage across it.
• The numbers assume an ideal battery. A real 9 V battery sags under larger loads, so you'd measure a little less than 90 mA.
• The checkout-line picture is a simplification, not how electrons really behave.
• "Double the current" is only true for two equal branches.
• Lower total resistance means more total current drawn from the source. That's why plugging too many devices into one household circuit can trip a breaker.

Answer to the comment question

Two six-ohm resistors in parallel. What's the total resistance? 3 ohms. For two equal resistors in parallel, divide one resistor by how many there are: 6 Ω ÷ 2 = 3 Ω. Check with the rule: 1/6 + 1/6 = 2/6 = 1/3, so R total = 3 Ω, less than either 6 Ω resistor, just as the parallel rule says.