Lessons · Engineering · series and parallel resistance
Series adds; parallel shares
Resistors in series add: R = R_1 + R_2. In parallel the reciprocals add: 1/R = 1/R_1 + 1/R_2, and the result is smaller than the smallest branch.
Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.
What it is for
A heater bank of six elements trips the breaker when the sixth is wired in. Six in parallel is a sixth of the resistance and six times the current, and the person wiring it thought resistance only ever went up.
How to think about it
Series: one path, add them. Parallel: several paths, add the reciprocals and flip back. Then sanity: a parallel total is always below the smallest branch, and if it is not, you forgot to flip.
Worked example
Series: R = R_1 + R_2. Parallel: 1/R = 1/R_1 + 1/R_2The two rules.
12 Ω and 6 Ω in series: R = 18 ΩOne path, add.
12 Ω and 6 Ω in parallel: 1/R = 1/12 + 1/6 = 3/12, so R = 4 ΩAdd the reciprocals, then flip back.
4 Ω is less than 6 Ω, the smaller branch. OKParallel is always less than the smallest branch. The check takes one glance.
Your turn
10 Ω and 10 Ω in parallel. Write the total.
1/R = 1/10 + 1/10, so R = Ω
Solve one, graded on the server
The trap
Forgetting to flip back. 1/12 + 1/6 = 0.25 is 1/R, not R. The resistance is 1 / 0.25 = 4 Ω, and a 0.25 Ω heater bank is a short circuit.