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First year Lesson 6 of 14 About 15 min

Parallel circuits

What you’ll learn

  • The three rules of a parallel circuit: same voltage, currents add, total resistance drops.
  • Three ways to find total resistance — equal branches, product over sum, and reciprocals.
  • Why every receptacle and light in a building is wired in parallel.
  • Why plugging in one more thing can trip a breaker.

A parallel circuit gives the current more than one path: each load is connected directly across the same two supply points. So every branch sees the full voltage, the branch currents add up to the total, and the total resistance comes out lower than any single branch. It is how every receptacle and light in a building is connected.

120 V 30 Ω 4 A 60 Ω 2 A 20 Ω 6 A 12 A 120 V across every branch · 4 + 2 + 6 = 12 A
Three branches, one voltage. The supply current is the sum of the branch currents, and 120 V ÷ 12 A says the whole circuit behaves like 10 Ω.

The three rules

  • VT = V1 = V2 = …one voltage
  • IT = I1 + I2 + …currents add
  • 1/RT = 1/R1 + 1/R2 + …reciprocals add

Three ways to find the total resistance

Equal branches: divide one branch by the number of branches. Four 100 Ω lamps in parallel act like 25 Ω.

Two branches, any values: product over sum. RT = (R1 × R2) ÷ (R1 + R2). For more than two, combine them two at a time.

Any number: add up the reciprocals (1 ÷ R for each), then take the reciprocal of the sum. Or skip the resistances completely: find each branch current, add them, and divide the voltage by the total.

1. The circuit in the drawing, two ways

  1. Branch currents: 120 ÷ 30 = 4 A, 120 ÷ 60 = 2 A, 120 ÷ 20 = 6 A.
  2. Total current: 4 + 2 + 6 = 12 A. Total resistance: 120 ÷ 12 = 10 Ω.
  3. Check with reciprocals: 1/30 + 1/60 + 1/20 = 2/60 + 1/60 + 3/60 = 6/60. Flip it: 60 ÷ 6 = 10 Ω ✓
  4. 10 Ω is less than the smallest branch (20 Ω), as it must be.

2. Product over sum

  1. A 6 Ω and a 3 Ω in parallel.
  2. (6 × 3) ÷ (6 + 3) = 18 ÷ 9 = 2 Ω.

3. Why the breaker tripped

  1. A kitchen circuit at 120 V on a 15 A breaker. The kettle is 1,500 W: 1,500 ÷ 120 = 12.5 A.
  2. Someone starts the 900 W toaster too: 900 ÷ 120 = 7.5 A.
  3. They are parallel branches, so the currents add: 12.5 + 7.5 = 20 A on one circuit — a third more than the 15 A breaker is built to carry, so it trips after a short time. Each appliance still has its full 120 V; it is the conductor and the breaker feeding them both that carry the total.
Series vs parallel, one line each

Series: one current, voltages add, resistance adds. Parallel: one voltage, currents add, resistance drops. Learn those two lines and you can do the next lesson.

Try one: 12 Ω, 12 Ω and 6 Ω in parallel on 24 V

Currents: 2 A + 2 A + 4 A = 8 A. RT = 24 ÷ 8 = 3 Ω. Check: 12 ∥ 12 = 6 Ω, and 6 ∥ 6 = 3 Ω ✓

En la obra

Tips from the job

  • Every receptacle and light on a branch circuit is a parallel branch. Add up the loads that run together and you have the current the circuit carries.
  • Load a circuit on paper before you load it for real: nameplate watts ÷ volts for each load, then add the amps.
  • A dead short is a parallel branch with almost no resistance. That is why a short trips the breaker instantly.
  • Try the interactive series vs parallel lighting diagram and pull a lamp out of each.

Common mistakes

  • Adding parallel resistances like series ones. In parallel the total is always less than the smallest branch — if your answer is bigger, start again.
  • Forgetting to take the reciprocal at the end of the 1/R method.
  • Assuming each branch gets a share of the voltage. Each branch gets all of it.
  • Using the product-over-sum shortcut on three resistors at once — it only works two at a time.

Check yourself

8 questions. Tap an answer — it is marked straight away and the reason opens under it. Get 80% or better and the lesson is ticked off on the year page.

Not started yet.

  1. Three loads are in parallel across 120 V. What voltage does each one see?

    Answer and why

    B. In parallel every branch is connected across the same two points, so every branch gets the full supply voltage.

  2. Branch currents of 3 A, 5 A and 4 A. What is the total current from the supply?

    Answer and why

    C. In parallel the branch currents add: 3 + 5 + 4 = 12 A. This is why plugging more things into one circuit eventually trips the breaker.

  3. Two 40 Ω resistors in parallel. Total resistance?

    Answer and why

    C. Equal resistors in parallel: divide one by how many there are. 40 ÷ 2 = 20 Ω.

  4. A 6 Ω and a 3 Ω resistor in parallel. Total resistance?

    Answer and why

    D. Product over sum: (6 × 3) ÷ (6 + 3) = 18 ÷ 9 = 2 Ω. It is less than the smallest branch, as it always must be.

  5. Adding another load in parallel to a circuit will…

    Answer and why

    B. Another branch is another path for current. More paths means less total resistance and more total current — the other branches carry on exactly as before.

  6. One lamp in a parallel lighting circuit burns out. The others…

    Answer and why

    B. Each branch has its own path from the supply. Opening one branch does not affect the voltage across the others.

  7. A 1,500 W kettle and a 900 W toaster run together on one 120 V circuit. Total current?

    Answer and why

    C. Kettle: 1,500 ÷ 120 = 12.5 A. Toaster: 900 ÷ 120 = 7.5 A. In parallel the currents add: 20 A.

  8. Which branch of a parallel circuit carries the most current?

    Answer and why

    B. Same voltage on every branch, so I = V ÷ R is largest where R is smallest. A short circuit is the extreme case: almost no resistance, huge current.

Preguntas frecuentes

Why is total resistance in parallel less than the smallest resistor?

Every branch you add is another path for current. Even a high-resistance branch lets a little more current through, so the supply sees more current for the same voltage — which is what lower resistance means. Two lanes of traffic move more cars than one, even if the second lane is slow.

Why are houses wired in parallel?

So every device gets the full supply voltage it was built for, and each one can be switched on or off (or fail) without affecting the others. In series, one lamp burning out would kill the circuit and every device would get only part of the voltage.

Ver también

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