ScienceAges 13-15

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 13-15

Series & parallel resistor networks

Take your time. Show your thinking.

1. Two resistors of 3 Ω and 22 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 3 Ω, R₂ = 22 Ω · R_eq = R₁ + R₂ = ?
2. Two resistors of 32 Ω and 96 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 32 Ω ∥ 96 Ω · 1/R_eq = 1/32 + 1/96
3. Two resistors of 12 Ω and 36 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 12 Ω ∥ 36 Ω · 1/R_eq = 1/12 + 1/36
4. Two resistors of 7 Ω and 4 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 7 Ω, R₂ = 4 Ω · R_eq = R₁ + R₂ = ?
5. Two resistors of 25 Ω and 3 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 25 Ω, R₂ = 3 Ω · R_eq = R₁ + R₂ = ?
6. Two resistors of 2 Ω and 18 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 2 Ω, R₂ = 18 Ω · R_eq = R₁ + R₂ = ?
7. Two resistors of 12 Ω and 13 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 12 Ω, R₂ = 13 Ω · R_eq = R₁ + R₂ = ?
8. Two resistors of 25 Ω and 14 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 25 Ω, R₂ = 14 Ω · R_eq = R₁ + R₂ = ?
9. 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
10. Two resistors of 15 Ω and 5 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 15 Ω, R₂ = 5 Ω · R_eq = R₁ + R₂ = ?
11. Two resistors of 11 Ω and 25 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 11 Ω, R₂ = 25 Ω · R_eq = R₁ + R₂ = ?
12. 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

12 questions · Seed 57 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 13-15

Series & parallel resistor networks

Answers and reasoning. Review before teaching.

1. Two resistors of 3 Ω and 22 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
25 Ω
In a series circuit, resistances add directly: R_eq = 3 Ω + 22 Ω = 25 Ω.
2. Two resistors of 32 Ω and 96 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
24 Ω
For two parallel resistors, R_eq = (32 × 96) ÷ (32 + 96) = 3072 ÷ 128 = 24 Ω.
3. Two resistors of 12 Ω and 36 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
9 Ω
For two parallel resistors, R_eq = (12 × 36) ÷ (12 + 36) = 432 ÷ 48 = 9 Ω.
4. Two resistors of 7 Ω and 4 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
11 Ω
In a series circuit, resistances add directly: R_eq = 7 Ω + 4 Ω = 11 Ω.
5. Two resistors of 25 Ω and 3 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
28 Ω
In a series circuit, resistances add directly: R_eq = 25 Ω + 3 Ω = 28 Ω.
6. Two resistors of 2 Ω and 18 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
20 Ω
In a series circuit, resistances add directly: R_eq = 2 Ω + 18 Ω = 20 Ω.
7. Two resistors of 12 Ω and 13 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
25 Ω
In a series circuit, resistances add directly: R_eq = 12 Ω + 13 Ω = 25 Ω.
8. Two resistors of 25 Ω and 14 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
39 Ω
In a series circuit, resistances add directly: R_eq = 25 Ω + 14 Ω = 39 Ω.
9. 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.
10. Two resistors of 15 Ω and 5 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
20 Ω
In a series circuit, resistances add directly: R_eq = 15 Ω + 5 Ω = 20 Ω.
11. Two resistors of 11 Ω and 25 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
36 Ω
In a series circuit, resistances add directly: R_eq = 11 Ω + 25 Ω = 36 Ω.
12. 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.

12 questions · Seed 57 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Series & parallel resistor networks

Take your time. Show your thinking.

1. Two resistors of 3 Ω and 22 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 3 Ω, R₂ = 22 Ω · R_eq = R₁ + R₂ = ?
2. Two resistors of 32 Ω and 96 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 32 Ω ∥ 96 Ω · 1/R_eq = 1/32 + 1/96
3. Two resistors of 12 Ω and 36 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 12 Ω ∥ 36 Ω · 1/R_eq = 1/12 + 1/36
4. Two resistors of 7 Ω and 4 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 7 Ω, R₂ = 4 Ω · R_eq = R₁ + R₂ = ?
5. Two resistors of 25 Ω and 3 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 25 Ω, R₂ = 3 Ω · R_eq = R₁ + R₂ = ?
6. Two resistors of 2 Ω and 18 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 2 Ω, R₂ = 18 Ω · R_eq = R₁ + R₂ = ?
7. Two resistors of 12 Ω and 13 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 12 Ω, R₂ = 13 Ω · R_eq = R₁ + R₂ = ?
8. Two resistors of 25 Ω and 14 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 25 Ω, R₂ = 14 Ω · R_eq = R₁ + R₂ = ?
9. 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
10. Two resistors of 15 Ω and 5 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 15 Ω, R₂ = 5 Ω · R_eq = R₁ + R₂ = ?
11. Two resistors of 11 Ω and 25 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 11 Ω, R₂ = 25 Ω · R_eq = R₁ + R₂ = ?
12. 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

12 questions · Seed 57 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Series & parallel resistor networks

Answers and reasoning. Review before teaching.

1. Two resistors of 3 Ω and 22 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
25 Ω
In a series circuit, resistances add directly: R_eq = 3 Ω + 22 Ω = 25 Ω.
2. Two resistors of 32 Ω and 96 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
24 Ω
For two parallel resistors, R_eq = (32 × 96) ÷ (32 + 96) = 3072 ÷ 128 = 24 Ω.
3. Two resistors of 12 Ω and 36 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
9 Ω
For two parallel resistors, R_eq = (12 × 36) ÷ (12 + 36) = 432 ÷ 48 = 9 Ω.
4. Two resistors of 7 Ω and 4 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
11 Ω
In a series circuit, resistances add directly: R_eq = 7 Ω + 4 Ω = 11 Ω.
5. Two resistors of 25 Ω and 3 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
28 Ω
In a series circuit, resistances add directly: R_eq = 25 Ω + 3 Ω = 28 Ω.
6. Two resistors of 2 Ω and 18 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
20 Ω
In a series circuit, resistances add directly: R_eq = 2 Ω + 18 Ω = 20 Ω.
7. Two resistors of 12 Ω and 13 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
25 Ω
In a series circuit, resistances add directly: R_eq = 12 Ω + 13 Ω = 25 Ω.
8. Two resistors of 25 Ω and 14 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
39 Ω
In a series circuit, resistances add directly: R_eq = 25 Ω + 14 Ω = 39 Ω.
9. 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.
10. Two resistors of 15 Ω and 5 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
20 Ω
In a series circuit, resistances add directly: R_eq = 15 Ω + 5 Ω = 20 Ω.
11. Two resistors of 11 Ω and 25 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
36 Ω
In a series circuit, resistances add directly: R_eq = 11 Ω + 25 Ω = 36 Ω.
12. 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.

12 questions · Seed 57 · Age guidance, not curriculum certification