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Series and parallel worksheet

Twelve resistor problems: series totals, parallel pairs, identical resistors in parallel, a series resistor feeding a parallel pair, the voltage across one resistor of a series string, and the current a parallel pair draws. The answer key shows each step, so a combination circuit can be checked one piece at a time.

Series and parallel worksheet · sheet #1

NameDateScore/ 12

series: R = R1 + R2 + R3two in parallel: R = R1 × R2 ÷ (R1 + R2)n equal in parallel: R ÷ ndivider: V1 = V × R1 ÷ (R1 + R2)

  1. Three resistors, 2 Ω, 22 Ω and 40 Ω, are in series. What is the total resistance?

  2. 60 Ω and 30 Ω are in parallel. What is the total resistance?

  3. 4 identical 40 Ω resistors are in parallel. What is the total resistance?

  4. R1 = 20 Ω is in series with 30 Ω and 15 Ω in parallel. What is the total resistance?

  5. 16 Ω and 6 Ω are in series across 24 V. What voltage is across the 16 Ω resistor?

  6. 10 Ω and 10 Ω are in parallel across 12 V. What total current does the supply deliver?

  7. Three resistors, 4 Ω, 17 Ω and 31 Ω, are in series. What is the total resistance?

  8. 12 Ω and 6 Ω are in parallel. What is the total resistance?

  9. 3 identical 10 Ω resistors are in parallel. What is the total resistance?

  10. R1 = 17 Ω is in series with 40 Ω and 10 Ω in parallel. What is the total resistance?

  11. 7 Ω and 21 Ω are in series across 48 V. What voltage is across the 7 Ω resistor?

  12. 36 Ω and 12 Ω are in parallel across 12 V. What total current does the supply deliver?

sparkytools.net/worksheets/series-parallel — free practice sheet. Practice numbers only; nothing here is a code-book value.

Answer key · Series and parallel worksheet · sheet #1

Show the answers and the working
  1. 64 Ω Series adds: 2 + 22 + 40 = 64 Ω
  2. 20 Ω Product over sum: 60 × 30 ÷ (60 + 30) = 1800 ÷ 90 = 20 Ω
  3. 10 Ω Equal resistors in parallel: 40 ÷ 4 = 10 Ω
  4. 30 Ω 30 ∥ 15 = 10 Ω; 20 + 10 = 30 Ω
  5. 17.45 V I = 24 ÷ (16 + 6) = 1.091 A; V = I × 16 = 17.45 V
  6. 2.4 A Each branch sees 12 V: 12 ÷ 10 + 12 ÷ 10 = 1.2 + 1.2 = 2.4 A
  7. 52 Ω Series adds: 4 + 17 + 31 = 52 Ω
  8. 4 Ω Product over sum: 12 × 6 ÷ (12 + 6) = 72 ÷ 18 = 4 Ω
  9. 3.33 Ω Equal resistors in parallel: 10 ÷ 3 = 3.33 Ω
  10. 25 Ω 40 ∥ 10 = 8 Ω; 17 + 8 = 25 Ω
  11. 12 V I = 48 ÷ (7 + 21) = 1.714 A; V = I × 7 = 12 V
  12. 1.33 A Each branch sees 12 V: 12 ÷ 36 + 12 ÷ 12 = 0.33 + 1 = 1.33 A

How to use it

  1. Print the sheet (or save it as a PDF from the print dialog). The answer key prints on its own page, so you can hand the sheet out and keep the key.
  2. Work every problem on paper, with the formula strip at the top, before you look at anything.
  3. Mark it from the key. For each miss, read the working line and find the exact step you did differently.
  4. Press New sheet for another twelve; the sheet number is in the link, so the same sheet can be printed again.

Worked example

A combination circuit, one piece at a time

  1. R1 = 8 Ω is in series with 12 Ω and 6 Ω in parallel, across 24 V. Find the total resistance and the current.
  2. Collapse the parallel pair first: 12 × 6 ÷ (12 + 6) = 72 ÷ 18 = 4 Ω.
  3. Now it is two in series: 8 + 4 = 12 Ω.
  4. Current from the supply: 24 ÷ 12 = 2 A. The pair drops 2 × 4 = 8 V, R1 drops 2 × 8 = 16 V — and 8 + 16 = 24 V, the supply. That check never lies.

Two in parallel always come out smaller than the smaller of the two. If your answer is bigger, you added instead.

Questions people ask

What order do I work a combination circuit in?

From the far end in: collapse each parallel group to one resistor, add the series pieces, and repeat until one resistor is left. Then come back out with the current to find each voltage.

Can I print a different sheet?

Yes. Press New sheet and you get another twelve problems with their own answer key; the sheet number goes into the link, so you can print it again later or send it to someone and they get the same sheet. Sheet #1 is always the one this page opens on.

Does it cost anything or need an account?

No. Every worksheet is free, prints from your own browser (or saves as a PDF from the print dialog), and needs no sign-up.

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