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 4 Ω and 6 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 4 Ω, R₂ = 6 Ω · R_eq = R₁ + R₂ = ?
2. 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
3. Two resistors of 9 Ω and 9 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 9 Ω, R₂ = 9 Ω · R_eq = R₁ + R₂ = ?
4. Two resistors of 7 Ω and 6 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 7 Ω, R₂ = 6 Ω · R_eq = R₁ + R₂ = ?
5. Two resistors of 6 Ω and 7 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 6 Ω, R₂ = 7 Ω · R_eq = R₁ + R₂ = ?
6. Two resistors of 5 Ω and 20 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 5 Ω ∥ 20 Ω · 1/R_eq = 1/5 + 1/20
7. Two resistors of 23 Ω and 11 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 23 Ω, R₂ = 11 Ω · R_eq = R₁ + R₂ = ?
8. Two resistors of 14 Ω and 24 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 14 Ω, R₂ = 24 Ω · R_eq = R₁ + R₂ = ?
9. Two resistors of 6 Ω and 16 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 6 Ω, R₂ = 16 Ω · R_eq = R₁ + R₂ = ?
10. Two resistors of 17 Ω and 5 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 17 Ω, R₂ = 5 Ω · R_eq = R₁ + R₂ = ?
11. Two resistors of 24 Ω and 48 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 24 Ω ∥ 48 Ω · 1/R_eq = 1/24 + 1/48
12. 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

12 questions · Seed 104730 · 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 4 Ω and 6 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
10 Ω
In a series circuit, resistances add directly: R_eq = 4 Ω + 6 Ω = 10 Ω.
2. 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.
3. Two resistors of 9 Ω and 9 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
18 Ω
In a series circuit, resistances add directly: R_eq = 9 Ω + 9 Ω = 18 Ω.
4. Two resistors of 7 Ω and 6 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
13 Ω
In a series circuit, resistances add directly: R_eq = 7 Ω + 6 Ω = 13 Ω.
5. Two resistors of 6 Ω and 7 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
13 Ω
In a series circuit, resistances add directly: R_eq = 6 Ω + 7 Ω = 13 Ω.
6. Two resistors of 5 Ω and 20 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
4 Ω
For two parallel resistors, R_eq = (5 × 20) ÷ (5 + 20) = 100 ÷ 25 = 4 Ω.
7. Two resistors of 23 Ω and 11 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
34 Ω
In a series circuit, resistances add directly: R_eq = 23 Ω + 11 Ω = 34 Ω.
8. Two resistors of 14 Ω and 24 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
38 Ω
In a series circuit, resistances add directly: R_eq = 14 Ω + 24 Ω = 38 Ω.
9. Two resistors of 6 Ω and 16 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
22 Ω
In a series circuit, resistances add directly: R_eq = 6 Ω + 16 Ω = 22 Ω.
10. Two resistors of 17 Ω and 5 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
22 Ω
In a series circuit, resistances add directly: R_eq = 17 Ω + 5 Ω = 22 Ω.
11. Two resistors of 24 Ω and 48 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
16 Ω
For two parallel resistors, R_eq = (24 × 48) ÷ (24 + 48) = 1152 ÷ 72 = 16 Ω.
12. 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.

12 questions · Seed 104730 · 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 4 Ω and 6 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 4 Ω, R₂ = 6 Ω · R_eq = R₁ + R₂ = ?
2. 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
3. Two resistors of 9 Ω and 9 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 9 Ω, R₂ = 9 Ω · R_eq = R₁ + R₂ = ?
4. Two resistors of 7 Ω and 6 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 7 Ω, R₂ = 6 Ω · R_eq = R₁ + R₂ = ?
5. Two resistors of 6 Ω and 7 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 6 Ω, R₂ = 7 Ω · R_eq = R₁ + R₂ = ?
6. Two resistors of 5 Ω and 20 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 5 Ω ∥ 20 Ω · 1/R_eq = 1/5 + 1/20
7. Two resistors of 23 Ω and 11 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 23 Ω, R₂ = 11 Ω · R_eq = R₁ + R₂ = ?
8. Two resistors of 14 Ω and 24 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 14 Ω, R₂ = 24 Ω · R_eq = R₁ + R₂ = ?
9. Two resistors of 6 Ω and 16 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 6 Ω, R₂ = 16 Ω · R_eq = R₁ + R₂ = ?
10. Two resistors of 17 Ω and 5 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 17 Ω, R₂ = 5 Ω · R_eq = R₁ + R₂ = ?
11. Two resistors of 24 Ω and 48 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 24 Ω ∥ 48 Ω · 1/R_eq = 1/24 + 1/48
12. 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

12 questions · Seed 104730 · 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 4 Ω and 6 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
10 Ω
In a series circuit, resistances add directly: R_eq = 4 Ω + 6 Ω = 10 Ω.
2. 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.
3. Two resistors of 9 Ω and 9 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
18 Ω
In a series circuit, resistances add directly: R_eq = 9 Ω + 9 Ω = 18 Ω.
4. Two resistors of 7 Ω and 6 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
13 Ω
In a series circuit, resistances add directly: R_eq = 7 Ω + 6 Ω = 13 Ω.
5. Two resistors of 6 Ω and 7 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
13 Ω
In a series circuit, resistances add directly: R_eq = 6 Ω + 7 Ω = 13 Ω.
6. Two resistors of 5 Ω and 20 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
4 Ω
For two parallel resistors, R_eq = (5 × 20) ÷ (5 + 20) = 100 ÷ 25 = 4 Ω.
7. Two resistors of 23 Ω and 11 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
34 Ω
In a series circuit, resistances add directly: R_eq = 23 Ω + 11 Ω = 34 Ω.
8. Two resistors of 14 Ω and 24 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
38 Ω
In a series circuit, resistances add directly: R_eq = 14 Ω + 24 Ω = 38 Ω.
9. Two resistors of 6 Ω and 16 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
22 Ω
In a series circuit, resistances add directly: R_eq = 6 Ω + 16 Ω = 22 Ω.
10. Two resistors of 17 Ω and 5 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
22 Ω
In a series circuit, resistances add directly: R_eq = 17 Ω + 5 Ω = 22 Ω.
11. Two resistors of 24 Ω and 48 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
16 Ω
For two parallel resistors, R_eq = (24 × 48) ÷ (24 + 48) = 1152 ÷ 72 = 16 Ω.
12. 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.

12 questions · Seed 104730 · Age guidance, not curriculum certification