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.
In beta. This lesson was written for Hone and has not yet been checked by a licensed engineer. Practice material, not professional advice. What that means.
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.