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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Worksheet StudioPractice pack · Ages 10-12

Series & parallel resistor networks

Take your time. Show your thinking.

1. Two resistors of 5 Ω and 17 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 5 Ω, R₂ = 17 Ω · R_eq = R₁ + R₂ = ?
2. Two resistors of 17 Ω and 10 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 17 Ω, R₂ = 10 Ω · R_eq = R₁ + R₂ = ?
3. Two resistors of 5 Ω and 5 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 5 Ω, R₂ = 5 Ω · R_eq = R₁ + R₂ = ?
4. 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
5. Two resistors of 20 Ω and 80 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 20 Ω ∥ 80 Ω · 1/R_eq = 1/20 + 1/80
6. Two resistors of 19 Ω and 16 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 19 Ω, R₂ = 16 Ω · R_eq = R₁ + R₂ = ?
7. 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
8. Two resistors of 21 Ω and 20 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 21 Ω, R₂ = 20 Ω · R_eq = R₁ + R₂ = ?
9. Two resistors of 14 Ω and 12 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 14 Ω, R₂ = 12 Ω · R_eq = R₁ + R₂ = ?
10. Two resistors of 11 Ω and 11 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 11 Ω, R₂ = 11 Ω · R_eq = R₁ + R₂ = ?
11. Two resistors of 8 Ω and 24 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 8 Ω ∥ 24 Ω · 1/R_eq = 1/8 + 1/24
12. 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

12 questions · Seed 44 · 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 5 Ω and 17 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
22 Ω
In a series circuit, resistances add directly: R_eq = 5 Ω + 17 Ω = 22 Ω.
2. Two resistors of 17 Ω and 10 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
27 Ω
In a series circuit, resistances add directly: R_eq = 17 Ω + 10 Ω = 27 Ω.
3. Two resistors of 5 Ω and 5 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
10 Ω
In a series circuit, resistances add directly: R_eq = 5 Ω + 5 Ω = 10 Ω.
4. 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.
5. Two resistors of 20 Ω and 80 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
16 Ω
For two parallel resistors, R_eq = (20 × 80) ÷ (20 + 80) = 1600 ÷ 100 = 16 Ω.
6. Two resistors of 19 Ω and 16 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
35 Ω
In a series circuit, resistances add directly: R_eq = 19 Ω + 16 Ω = 35 Ω.
7. 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.
8. Two resistors of 21 Ω and 20 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
41 Ω
In a series circuit, resistances add directly: R_eq = 21 Ω + 20 Ω = 41 Ω.
9. Two resistors of 14 Ω and 12 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
26 Ω
In a series circuit, resistances add directly: R_eq = 14 Ω + 12 Ω = 26 Ω.
10. Two resistors of 11 Ω and 11 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
22 Ω
In a series circuit, resistances add directly: R_eq = 11 Ω + 11 Ω = 22 Ω.
11. Two resistors of 8 Ω and 24 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
6 Ω
For two parallel resistors, R_eq = (8 × 24) ÷ (8 + 24) = 192 ÷ 32 = 6 Ω.
12. 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.

12 questions · Seed 44 · 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 5 Ω and 17 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 5 Ω, R₂ = 17 Ω · R_eq = R₁ + R₂ = ?
2. Two resistors of 17 Ω and 10 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 17 Ω, R₂ = 10 Ω · R_eq = R₁ + R₂ = ?
3. Two resistors of 5 Ω and 5 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 5 Ω, R₂ = 5 Ω · R_eq = R₁ + R₂ = ?
4. 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
5. Two resistors of 20 Ω and 80 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 20 Ω ∥ 80 Ω · 1/R_eq = 1/20 + 1/80
6. Two resistors of 19 Ω and 16 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 19 Ω, R₂ = 16 Ω · R_eq = R₁ + R₂ = ?
7. 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
8. Two resistors of 21 Ω and 20 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 21 Ω, R₂ = 20 Ω · R_eq = R₁ + R₂ = ?
9. Two resistors of 14 Ω and 12 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 14 Ω, R₂ = 12 Ω · R_eq = R₁ + R₂ = ?
10. Two resistors of 11 Ω and 11 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 11 Ω, R₂ = 11 Ω · R_eq = R₁ + R₂ = ?
11. Two resistors of 8 Ω and 24 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 8 Ω ∥ 24 Ω · 1/R_eq = 1/8 + 1/24
12. 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

12 questions · Seed 44 · 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 5 Ω and 17 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
22 Ω
In a series circuit, resistances add directly: R_eq = 5 Ω + 17 Ω = 22 Ω.
2. Two resistors of 17 Ω and 10 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
27 Ω
In a series circuit, resistances add directly: R_eq = 17 Ω + 10 Ω = 27 Ω.
3. Two resistors of 5 Ω and 5 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
10 Ω
In a series circuit, resistances add directly: R_eq = 5 Ω + 5 Ω = 10 Ω.
4. 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.
5. Two resistors of 20 Ω and 80 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
16 Ω
For two parallel resistors, R_eq = (20 × 80) ÷ (20 + 80) = 1600 ÷ 100 = 16 Ω.
6. Two resistors of 19 Ω and 16 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
35 Ω
In a series circuit, resistances add directly: R_eq = 19 Ω + 16 Ω = 35 Ω.
7. 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.
8. Two resistors of 21 Ω and 20 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
41 Ω
In a series circuit, resistances add directly: R_eq = 21 Ω + 20 Ω = 41 Ω.
9. Two resistors of 14 Ω and 12 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
26 Ω
In a series circuit, resistances add directly: R_eq = 14 Ω + 12 Ω = 26 Ω.
10. Two resistors of 11 Ω and 11 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
22 Ω
In a series circuit, resistances add directly: R_eq = 11 Ω + 11 Ω = 22 Ω.
11. Two resistors of 8 Ω and 24 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
6 Ω
For two parallel resistors, R_eq = (8 × 24) ÷ (8 + 24) = 192 ÷ 32 = 6 Ω.
12. 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.

12 questions · Seed 44 · Age guidance, not curriculum certification