Lessons · Electrical · parallel circuits
Parallel: more paths, less resistance
In parallel every branch sees the full voltage, the branch currents add, and the total resistance is always 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
Every receptacle on a kitchen circuit is a parallel branch. The toaster does not care what the kettle is doing, but the wire feeding both of them carries the sum, and that sum is what trips the breaker.
How to think about it
Two branches: multiply them, divide by their sum. Equal branches: one branch divided by how many. Anything else: add the reciprocals and flip. Then check: the answer must be smaller than the smallest branch or you have made a mistake.
Worked example
R = (20 × 30) / (20 + 30) = 600 / 50 = 12 ΩTwo branches: product over sum. Smaller than 20, as it must be.
I = 120 V / 12 Ω = 10 AThe current the feeding wire carries.
I through the 20 Ω = 120 / 20 = 6 AEach branch sees the full 120 V. Six amps here.
I through the 30 Ω = 120 / 30 = 4 AAnd four here. 6 + 4 = 10: the branch currents add up to what the feed carries.
Four 100 Ω lamps: R = 100 / 4 = 25 ΩEqual branches: divide by the count.
Your turn
Two 8 Ω branches. Write the total.
R = (8 × 8) / (8 + ) = 4 Ω
Solve one, graded on the server
The trap
Adding parallel resistances the way you add series ones. Two 12 Ω heaters side by side are 6 Ω, not 24 Ω. Doubling the paths halves the resistance and doubles the current in the feed.