Parallel circuits

Two 12 Ω bulbs side by side on 6 V each take 0.5 A, so the battery supplies 1 A: twice as much as for one bulb.

Several paths, the same voltage

In a parallel circuit each part gets its own branch, joined directly across the battery. The ends of every branch connect to the same two wires, so every branch has the full battery voltage across it. That is the first rule of parallel circuits. The second rule is about current: the current from the battery splits at the first junction, some going down each branch, and joins up again at the other side. The branch currents add up to the total. No charge is lost at a junction; what comes in goes out.

Adding a branch lowers the total resistance

Each branch follows Ohm's law on its own: I₁ = V ÷ R₁, I₂ = V ÷ R₂. The total current is the sum, V ÷ R₁ + V ÷ R₂ + ..., and the single resistor that would draw the same current from the battery satisfies 1 ÷ R = 1 ÷ R₁ + 1 ÷ R₂ + 1 ÷ R₃ + ... . This total is always smaller than the smallest branch. It sounds odd at first, but it makes sense: every extra branch is one more way for charge to get through, like opening another checkout in a shop. Two 12 Ω bulbs in parallel act like 6 Ω; three act like 4 Ω. For two branches there is a shortcut, R = R₁R₂ ÷ (R₁ + R₂): 6 Ω and 12 Ω give 72 ÷ 18 = 4 Ω.

OpenStax repeats its series example in parallel: 1.00 Ω, 6.00 Ω and 13.0 Ω across 12.0 V. Each now has the full 12.0 V, so the currents are 12.0 A, 2.00 A and 0.923 A, adding to 14.9 A. The total resistance is 0.804 Ω, smaller than the 1.00 Ω branch. Compare with the series circuit, where the same three resistors drew only 0.600 A. In parallel the smallest resistor takes the biggest current, the opposite of series, where the biggest resistor took the biggest voltage.

Why houses are wired in parallel

Every socket and light in a house is on its own branch across the supply. That way each appliance gets the full supply voltage it was designed for, each can be switched on and off without affecting the others, and a dead lamp does not turn off the fridge. The cost is that each new appliance adds current to the wires that feed the branches. The supply wires and the fuse or breaker carry the total, so switching on many high-power appliances at once can push that total above a safe limit. The last unit of the course comes back to this.

Series and parallel together

Real circuits mix both. Solve them a piece at a time: first combine the parallel group into one resistance, then add it to whatever is in series with it. In the second lab below, L1 is in series with a parallel pair L2 and L3, all 12 Ω. The pair acts like 6 Ω, so the total is 12 + 6 = 18 Ω and the battery current is 6 ÷ 18 ≈ 0.333 A. All of that flows through L1, which takes 0.333 × 12 = 4 V. The remaining 2 V sits across the pair, so L2 and L3 each carry 2 ÷ 12 ≈ 0.167 A. L1 is clearly the brightest, which you can check in the lab.