sparkytools

First year Lesson 5 of 14 About 15 min

Series circuits

What you’ll learn

  • The three rules of a series circuit: one current, resistances add, voltage drops add up to the supply.
  • How to work out the current and every voltage drop in a series string.
  • Why the biggest resistance gets the biggest share of the voltage.
  • Why an open in series reads full voltage across it — the first troubleshooting trick.

A series circuit has one path: the current goes through every part, one after the other. That single fact gives you three rules — the current is the same everywhere, the resistances add up, and the voltage drops add up to the supply — and those three rules solve every series circuit you will meet.

120 V 10 Ω 20 V 20 Ω 40 V 30 Ω 60 V I = 2 A everywhere 20 + 40 + 60 = 120 V
One path, one current. The drops share out the supply in proportion to the resistances.

The three rules

  • IT = I1 = I2 = …one current
  • RT = R1 + R2 + …resistances add
  • VT = V1 + V2 + …drops add to the supply

Power adds too: the total power is the sum of what each part dissipates, and it also equals the supply voltage times the current.

The method

  1. Add the resistances to get RT.
  2. Find the current: I = VT ÷ RT. That current flows through every part.
  3. Find each drop: V = I × R for each resistor.
  4. Check: the drops add up to the supply.

1. The circuit in the drawing

  1. RT = 10 + 20 + 30 = 60 Ω.
  2. I = 120 ÷ 60 = 2 A, through all three.
  3. Drops: 2 × 10 = 20 V, 2 × 20 = 40 V, 2 × 30 = 60 V. Check: 20 + 40 + 60 = 120 V ✓
  4. Powers: 20 × 2 = 40 W, 40 × 2 = 80 W, 60 × 2 = 120 W. Total 240 W = 120 V × 2 A ✓

2. A voltage divider

  1. 24 V across a 1 kΩ and a 2 kΩ resistor in series. RT = 3 kΩ = 3,000 Ω.
  2. I = 24 ÷ 3,000 = 0.008 A = 8 mA.
  3. V1 = 0.008 × 1,000 = 8 V; V2 = 0.008 × 2,000 = 16 V. The 2 kΩ, twice the resistance, takes twice the voltage.

3. A bad connection is a series resistor

  1. A 120 V heater of 12 Ω has a corroded splice of 0.5 Ω in series with it. RT = 12.5 Ω.
  2. I = 120 ÷ 12.5 = 9.6 A (instead of 10 A).
  3. Drop at the splice: 9.6 × 0.5 = 4.8 V, heat at the splice: 9.6 × 4.8 ≈ 46 W. The heater gets 115.2 V. That splice is getting hot.

Finding an open in series

Open a series circuit anywhere and the current stops. With no current, every good part has V = I × R = 0 across it. So the whole supply voltage appears across the open — the broken lamp, the open switch, the loose connection. Measure across each part in turn with the power on (and the right PPE and meter): the one that reads the supply is the open one.

Remember it this way

Across a closed switch: 0 V. Across an open switch: full voltage. The same is true of any open in a series path — which is exactly how motor control circuits are traced.

Try one: 48 V across 4 Ω, 8 Ω and 12 Ω in series

RT = 24 Ω, I = 48 ÷ 24 = 2 A. Drops: 8 V, 16 V, 24 V — they add to 48 V.

On the job

Tips from the job

  • Switches, fuses, overload contacts and the load are all in series with each other. That is why one open contact anywhere stops a whole control circuit.
  • A loose or corroded connection is a resistor in series with the load: it steals voltage from the load and turns it into heat.
  • To find an open in a series path, measure across each part with the power on: the good parts read about 0 V, the open reads the full supply.
  • Practise the arithmetic on the series / parallel drill until you do it without thinking.

Common mistakes

  • Thinking current “gets used up” along the string, so the last resistor gets less. It gets exactly the same current.
  • Adding the voltage drops and getting a number different from the supply — recheck the arithmetic; they must match.
  • Wiring receptacles or lights in series by mistake, then wondering why each only gets part of the voltage.
  • Measuring resistance of a component while it is still in circuit and powered.

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 resistors of 10 Ω, 15 Ω and 25 Ω are in series. What is the total resistance?

    Answer and why

    C. In series the resistances simply add: 10 + 15 + 25 = 50 Ω.

  2. That 50 Ω string is connected to 100 V. What current flows through the 15 Ω resistor?

    Answer and why

    A. There is only one path, so the current is the same everywhere: I = V ÷ RT = 100 ÷ 50 = 2 A through every resistor.

  3. And the voltage across the 25 Ω resistor?

    Answer and why

    C. V = I × R = 2 × 25 = 50 V. The drops are 20 V, 30 V and 50 V, and they add up to the 100 V supply.

  4. In a series circuit, the largest resistance has…

    Answer and why

    C. Same current through all of them, so V = I × R is biggest where R is biggest. The biggest resistor gets the biggest share of the voltage — and of the power.

  5. One lamp in a series string burns open. What happens?

    Answer and why

    B. Series has one path. Open it anywhere and the current stops everywhere.

  6. With that lamp open, you measure across it with the supply on. What do you read?

    Answer and why

    B. With no current flowing, none of the good lamps drop any voltage (V = I × R = 0), so the whole supply appears across the gap. Full voltage across an open is how you find it.

  7. A string of 40 identical lamps runs on 120 V. What is the voltage across each lamp?

    Answer and why

    C. Identical loads in series share the voltage equally: 120 ÷ 40 = 3 V each.

  8. Adding another resistor in series to a circuit will…

    Answer and why

    B. Another resistor in series adds to the total resistance, and with the same voltage, more resistance means less current.

Questions people ask

Why is the current the same everywhere in a series circuit?

Because there is only one path, and charge does not pile up or vanish anywhere along it. Every amp that goes into the first resistor has to come out and go through the next. The current is set by the total resistance of the whole string.

Where are series circuits used in real wiring?

Branch circuit loads are almost never in series with each other — they are in parallel. But the parts that control a load are in series with it: the breaker, the switch, the load, the connections. Control circuits are long series paths of contacts. Old holiday light strings were series, which is why one bad bulb killed the string.

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