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 18 Ω and 90 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 18 Ω ∥ 90 Ω · 1/R_eq = 1/18 + 1/90
2. 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
3. Two resistors of 16 Ω and 48 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 16 Ω ∥ 48 Ω · 1/R_eq = 1/16 + 1/48
4. Two resistors of 3 Ω and 3 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 3 Ω, R₂ = 3 Ω · R_eq = R₁ + R₂ = ?
5. Two resistors of 20 Ω and 14 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 20 Ω, R₂ = 14 Ω · R_eq = R₁ + R₂ = ?
6. Two resistors of 6 Ω and 8 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 6 Ω, R₂ = 8 Ω · R_eq = R₁ + R₂ = ?
7. Two resistors of 30 Ω and 60 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 30 Ω ∥ 60 Ω · 1/R_eq = 1/30 + 1/60
8. Two resistors of 20 Ω and 60 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 20 Ω ∥ 60 Ω · 1/R_eq = 1/20 + 1/60
9. Two resistors of 20 Ω and 19 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 20 Ω, R₂ = 19 Ω · R_eq = R₁ + R₂ = ?
10. Two resistors of 8 Ω and 2 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 8 Ω, R₂ = 2 Ω · R_eq = R₁ + R₂ = ?
11. Two resistors of 23 Ω and 14 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 23 Ω, R₂ = 14 Ω · R_eq = R₁ + R₂ = ?
12. Two resistors of 8 Ω and 17 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 8 Ω, R₂ = 17 Ω · R_eq = R₁ + R₂ = ?

12 questions · Seed 55 · 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 18 Ω and 90 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
15 Ω
For two parallel resistors, R_eq = (18 × 90) ÷ (18 + 90) = 1620 ÷ 108 = 15 Ω.
2. 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.
3. Two resistors of 16 Ω and 48 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
12 Ω
For two parallel resistors, R_eq = (16 × 48) ÷ (16 + 48) = 768 ÷ 64 = 12 Ω.
4. Two resistors of 3 Ω and 3 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
6 Ω
In a series circuit, resistances add directly: R_eq = 3 Ω + 3 Ω = 6 Ω.
5. Two resistors of 20 Ω and 14 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
34 Ω
In a series circuit, resistances add directly: R_eq = 20 Ω + 14 Ω = 34 Ω.
6. Two resistors of 6 Ω and 8 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
14 Ω
In a series circuit, resistances add directly: R_eq = 6 Ω + 8 Ω = 14 Ω.
7. Two resistors of 30 Ω and 60 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
20 Ω
For two parallel resistors, R_eq = (30 × 60) ÷ (30 + 60) = 1800 ÷ 90 = 20 Ω.
8. Two resistors of 20 Ω and 60 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
15 Ω
For two parallel resistors, R_eq = (20 × 60) ÷ (20 + 60) = 1200 ÷ 80 = 15 Ω.
9. Two resistors of 20 Ω and 19 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
39 Ω
In a series circuit, resistances add directly: R_eq = 20 Ω + 19 Ω = 39 Ω.
10. Two resistors of 8 Ω and 2 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
10 Ω
In a series circuit, resistances add directly: R_eq = 8 Ω + 2 Ω = 10 Ω.
11. Two resistors of 23 Ω and 14 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
37 Ω
In a series circuit, resistances add directly: R_eq = 23 Ω + 14 Ω = 37 Ω.
12. Two resistors of 8 Ω and 17 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
25 Ω
In a series circuit, resistances add directly: R_eq = 8 Ω + 17 Ω = 25 Ω.

12 questions · Seed 55 · 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 18 Ω and 90 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 18 Ω ∥ 90 Ω · 1/R_eq = 1/18 + 1/90
2. 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
3. Two resistors of 16 Ω and 48 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 16 Ω ∥ 48 Ω · 1/R_eq = 1/16 + 1/48
4. Two resistors of 3 Ω and 3 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 3 Ω, R₂ = 3 Ω · R_eq = R₁ + R₂ = ?
5. Two resistors of 20 Ω and 14 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 20 Ω, R₂ = 14 Ω · R_eq = R₁ + R₂ = ?
6. Two resistors of 6 Ω and 8 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 6 Ω, R₂ = 8 Ω · R_eq = R₁ + R₂ = ?
7. Two resistors of 30 Ω and 60 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 30 Ω ∥ 60 Ω · 1/R_eq = 1/30 + 1/60
8. Two resistors of 20 Ω and 60 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 20 Ω ∥ 60 Ω · 1/R_eq = 1/20 + 1/60
9. Two resistors of 20 Ω and 19 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 20 Ω, R₂ = 19 Ω · R_eq = R₁ + R₂ = ?
10. Two resistors of 8 Ω and 2 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 8 Ω, R₂ = 2 Ω · R_eq = R₁ + R₂ = ?
11. Two resistors of 23 Ω and 14 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 23 Ω, R₂ = 14 Ω · R_eq = R₁ + R₂ = ?
12. Two resistors of 8 Ω and 17 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 8 Ω, R₂ = 17 Ω · R_eq = R₁ + R₂ = ?

12 questions · Seed 55 · 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 18 Ω and 90 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
15 Ω
For two parallel resistors, R_eq = (18 × 90) ÷ (18 + 90) = 1620 ÷ 108 = 15 Ω.
2. 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.
3. Two resistors of 16 Ω and 48 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
12 Ω
For two parallel resistors, R_eq = (16 × 48) ÷ (16 + 48) = 768 ÷ 64 = 12 Ω.
4. Two resistors of 3 Ω and 3 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
6 Ω
In a series circuit, resistances add directly: R_eq = 3 Ω + 3 Ω = 6 Ω.
5. Two resistors of 20 Ω and 14 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
34 Ω
In a series circuit, resistances add directly: R_eq = 20 Ω + 14 Ω = 34 Ω.
6. Two resistors of 6 Ω and 8 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
14 Ω
In a series circuit, resistances add directly: R_eq = 6 Ω + 8 Ω = 14 Ω.
7. Two resistors of 30 Ω and 60 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
20 Ω
For two parallel resistors, R_eq = (30 × 60) ÷ (30 + 60) = 1800 ÷ 90 = 20 Ω.
8. Two resistors of 20 Ω and 60 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
15 Ω
For two parallel resistors, R_eq = (20 × 60) ÷ (20 + 60) = 1200 ÷ 80 = 15 Ω.
9. Two resistors of 20 Ω and 19 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
39 Ω
In a series circuit, resistances add directly: R_eq = 20 Ω + 19 Ω = 39 Ω.
10. Two resistors of 8 Ω and 2 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
10 Ω
In a series circuit, resistances add directly: R_eq = 8 Ω + 2 Ω = 10 Ω.
11. Two resistors of 23 Ω and 14 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
37 Ω
In a series circuit, resistances add directly: R_eq = 23 Ω + 14 Ω = 37 Ω.
12. Two resistors of 8 Ω and 17 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
25 Ω
In a series circuit, resistances add directly: R_eq = 8 Ω + 17 Ω = 25 Ω.

12 questions · Seed 55 · Age guidance, not curriculum certification