ScienceAges 10-12

Series & parallel resistor networks

Calculate equivalent resistance for resistors in series (R₁ + R₂) or in parallel ((R₁ × R₂) ÷ (R₁ + R₂)). Review suitability for your learners before teaching.

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Age band:Ages 10-12 Ages 13-15

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Worksheet StudioPractice pack · Ages 10-12

Series & parallel resistor networks

Take your time. Show your thinking.

1. Two resistors of 24 Ω and 72 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 24 Ω ∥ 72 Ω · 1/R_eq = 1/24 + 1/72
2. Two resistors of 12 Ω and 2 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 12 Ω, R₂ = 2 Ω · R_eq = R₁ + R₂ = ?
3. Two resistors of 20 Ω and 9 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 20 Ω, R₂ = 9 Ω · R_eq = R₁ + R₂ = ?
4. Two resistors of 60 Ω and 120 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 60 Ω ∥ 120 Ω · 1/R_eq = 1/60 + 1/120
5. Two resistors of 6 Ω and 12 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 6 Ω ∥ 12 Ω · 1/R_eq = 1/6 + 1/12
6. Two resistors of 18 Ω and 16 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 18 Ω, R₂ = 16 Ω · R_eq = R₁ + R₂ = ?
7. Two resistors of 15 Ω and 25 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 15 Ω, R₂ = 25 Ω · R_eq = R₁ + R₂ = ?
8. Two resistors of 8 Ω and 18 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 8 Ω, R₂ = 18 Ω · R_eq = R₁ + R₂ = ?
9. Two resistors of 40 Ω and 40 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 40 Ω ∥ 40 Ω · 1/R_eq = 1/40 + 1/40
10. Two resistors of 60 Ω and 60 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 60 Ω ∥ 60 Ω · 1/R_eq = 1/60 + 1/60
11. Two resistors of 13 Ω and 16 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 13 Ω, R₂ = 16 Ω · R_eq = R₁ + R₂ = ?
12. Two resistors of 36 Ω and 72 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 36 Ω ∥ 72 Ω · 1/R_eq = 1/36 + 1/72

12 questions · Seed 47 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 10-12

Series & parallel resistor networks

Answers and reasoning. Review before teaching.

1. Two resistors of 24 Ω and 72 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
18 Ω
For two parallel resistors, R_eq = (24 × 72) ÷ (24 + 72) = 1728 ÷ 96 = 18 Ω.
2. Two resistors of 12 Ω and 2 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
14 Ω
In a series circuit, resistances add directly: R_eq = 12 Ω + 2 Ω = 14 Ω.
3. Two resistors of 20 Ω and 9 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
29 Ω
In a series circuit, resistances add directly: R_eq = 20 Ω + 9 Ω = 29 Ω.
4. Two resistors of 60 Ω and 120 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
40 Ω
For two parallel resistors, R_eq = (60 × 120) ÷ (60 + 120) = 7200 ÷ 180 = 40 Ω.
5. Two resistors of 6 Ω and 12 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
4 Ω
For two parallel resistors, R_eq = (6 × 12) ÷ (6 + 12) = 72 ÷ 18 = 4 Ω.
6. Two resistors of 18 Ω and 16 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
34 Ω
In a series circuit, resistances add directly: R_eq = 18 Ω + 16 Ω = 34 Ω.
7. Two resistors of 15 Ω and 25 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
40 Ω
In a series circuit, resistances add directly: R_eq = 15 Ω + 25 Ω = 40 Ω.
8. Two resistors of 8 Ω and 18 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
26 Ω
In a series circuit, resistances add directly: R_eq = 8 Ω + 18 Ω = 26 Ω.
9. Two resistors of 40 Ω and 40 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
20 Ω
For two parallel resistors, R_eq = (40 × 40) ÷ (40 + 40) = 1600 ÷ 80 = 20 Ω.
10. Two resistors of 60 Ω and 60 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
30 Ω
For two parallel resistors, R_eq = (60 × 60) ÷ (60 + 60) = 3600 ÷ 120 = 30 Ω.
11. Two resistors of 13 Ω and 16 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
29 Ω
In a series circuit, resistances add directly: R_eq = 13 Ω + 16 Ω = 29 Ω.
12. Two resistors of 36 Ω and 72 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
24 Ω
For two parallel resistors, R_eq = (36 × 72) ÷ (36 + 72) = 2592 ÷ 108 = 24 Ω.

12 questions · Seed 47 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 10-12

Series & parallel resistor networks

Take your time. Show your thinking.

1. Two resistors of 24 Ω and 72 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 24 Ω ∥ 72 Ω · 1/R_eq = 1/24 + 1/72
2. Two resistors of 12 Ω and 2 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 12 Ω, R₂ = 2 Ω · R_eq = R₁ + R₂ = ?
3. Two resistors of 20 Ω and 9 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 20 Ω, R₂ = 9 Ω · R_eq = R₁ + R₂ = ?
4. Two resistors of 60 Ω and 120 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 60 Ω ∥ 120 Ω · 1/R_eq = 1/60 + 1/120
5. Two resistors of 6 Ω and 12 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 6 Ω ∥ 12 Ω · 1/R_eq = 1/6 + 1/12
6. Two resistors of 18 Ω and 16 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 18 Ω, R₂ = 16 Ω · R_eq = R₁ + R₂ = ?
7. Two resistors of 15 Ω and 25 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 15 Ω, R₂ = 25 Ω · R_eq = R₁ + R₂ = ?
8. Two resistors of 8 Ω and 18 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 8 Ω, R₂ = 18 Ω · R_eq = R₁ + R₂ = ?
9. Two resistors of 40 Ω and 40 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 40 Ω ∥ 40 Ω · 1/R_eq = 1/40 + 1/40
10. Two resistors of 60 Ω and 60 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 60 Ω ∥ 60 Ω · 1/R_eq = 1/60 + 1/60
11. Two resistors of 13 Ω and 16 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 13 Ω, R₂ = 16 Ω · R_eq = R₁ + R₂ = ?
12. Two resistors of 36 Ω and 72 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 36 Ω ∥ 72 Ω · 1/R_eq = 1/36 + 1/72

12 questions · Seed 47 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 10-12

Series & parallel resistor networks

Answers and reasoning. Review before teaching.

1. Two resistors of 24 Ω and 72 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
18 Ω
For two parallel resistors, R_eq = (24 × 72) ÷ (24 + 72) = 1728 ÷ 96 = 18 Ω.
2. Two resistors of 12 Ω and 2 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
14 Ω
In a series circuit, resistances add directly: R_eq = 12 Ω + 2 Ω = 14 Ω.
3. Two resistors of 20 Ω and 9 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
29 Ω
In a series circuit, resistances add directly: R_eq = 20 Ω + 9 Ω = 29 Ω.
4. Two resistors of 60 Ω and 120 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
40 Ω
For two parallel resistors, R_eq = (60 × 120) ÷ (60 + 120) = 7200 ÷ 180 = 40 Ω.
5. Two resistors of 6 Ω and 12 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
4 Ω
For two parallel resistors, R_eq = (6 × 12) ÷ (6 + 12) = 72 ÷ 18 = 4 Ω.
6. Two resistors of 18 Ω and 16 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
34 Ω
In a series circuit, resistances add directly: R_eq = 18 Ω + 16 Ω = 34 Ω.
7. Two resistors of 15 Ω and 25 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
40 Ω
In a series circuit, resistances add directly: R_eq = 15 Ω + 25 Ω = 40 Ω.
8. Two resistors of 8 Ω and 18 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
26 Ω
In a series circuit, resistances add directly: R_eq = 8 Ω + 18 Ω = 26 Ω.
9. Two resistors of 40 Ω and 40 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
20 Ω
For two parallel resistors, R_eq = (40 × 40) ÷ (40 + 40) = 1600 ÷ 80 = 20 Ω.
10. Two resistors of 60 Ω and 60 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
30 Ω
For two parallel resistors, R_eq = (60 × 60) ÷ (60 + 60) = 3600 ÷ 120 = 30 Ω.
11. Two resistors of 13 Ω and 16 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
29 Ω
In a series circuit, resistances add directly: R_eq = 13 Ω + 16 Ω = 29 Ω.
12. Two resistors of 36 Ω and 72 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
24 Ω
For two parallel resistors, R_eq = (36 × 72) ÷ (36 + 72) = 2592 ÷ 108 = 24 Ω.

12 questions · Seed 47 · Age guidance, not curriculum certification