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 20 Ω and 24 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 20 Ω, R₂ = 24 Ω · R_eq = R₁ + R₂ = ?
2. Two resistors of 6 Ω and 6 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 6 Ω, R₂ = 6 Ω · R_eq = R₁ + R₂ = ?
3. Two resistors of 45 Ω and 90 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 45 Ω ∥ 90 Ω · 1/R_eq = 1/45 + 1/90
4. Two resistors of 3 Ω and 5 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 3 Ω, R₂ = 5 Ω · R_eq = R₁ + R₂ = ?
5. Two resistors of 75 Ω and 150 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 75 Ω ∥ 150 Ω · 1/R_eq = 1/75 + 1/150
6. Two resistors of 6 Ω and 30 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 6 Ω ∥ 30 Ω · 1/R_eq = 1/6 + 1/30
7. Two resistors of 11 Ω and 18 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 11 Ω, R₂ = 18 Ω · R_eq = R₁ + R₂ = ?
8. Two resistors of 18 Ω and 36 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 18 Ω ∥ 36 Ω · 1/R_eq = 1/18 + 1/36
9. Two resistors of 30 Ω and 120 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 30 Ω ∥ 120 Ω · 1/R_eq = 1/30 + 1/120
10. Two resistors of 36 Ω and 180 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 36 Ω ∥ 180 Ω · 1/R_eq = 1/36 + 1/180
11. Two resistors of 24 Ω and 17 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 24 Ω, R₂ = 17 Ω · R_eq = R₁ + R₂ = ?
12. Two resistors of 18 Ω and 15 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 18 Ω, R₂ = 15 Ω · R_eq = R₁ + R₂ = ?

12 questions · Seed 58 · 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 20 Ω and 24 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
44 Ω
In a series circuit, resistances add directly: R_eq = 20 Ω + 24 Ω = 44 Ω.
2. Two resistors of 6 Ω and 6 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
12 Ω
In a series circuit, resistances add directly: R_eq = 6 Ω + 6 Ω = 12 Ω.
3. Two resistors of 45 Ω and 90 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
30 Ω
For two parallel resistors, R_eq = (45 × 90) ÷ (45 + 90) = 4050 ÷ 135 = 30 Ω.
4. Two resistors of 3 Ω and 5 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
8 Ω
In a series circuit, resistances add directly: R_eq = 3 Ω + 5 Ω = 8 Ω.
5. Two resistors of 75 Ω and 150 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
50 Ω
For two parallel resistors, R_eq = (75 × 150) ÷ (75 + 150) = 11250 ÷ 225 = 50 Ω.
6. Two resistors of 6 Ω and 30 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
5 Ω
For two parallel resistors, R_eq = (6 × 30) ÷ (6 + 30) = 180 ÷ 36 = 5 Ω.
7. Two resistors of 11 Ω and 18 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
29 Ω
In a series circuit, resistances add directly: R_eq = 11 Ω + 18 Ω = 29 Ω.
8. Two resistors of 18 Ω and 36 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
12 Ω
For two parallel resistors, R_eq = (18 × 36) ÷ (18 + 36) = 648 ÷ 54 = 12 Ω.
9. Two resistors of 30 Ω and 120 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
24 Ω
For two parallel resistors, R_eq = (30 × 120) ÷ (30 + 120) = 3600 ÷ 150 = 24 Ω.
10. Two resistors of 36 Ω and 180 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
30 Ω
For two parallel resistors, R_eq = (36 × 180) ÷ (36 + 180) = 6480 ÷ 216 = 30 Ω.
11. Two resistors of 24 Ω and 17 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
41 Ω
In a series circuit, resistances add directly: R_eq = 24 Ω + 17 Ω = 41 Ω.
12. Two resistors of 18 Ω and 15 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
33 Ω
In a series circuit, resistances add directly: R_eq = 18 Ω + 15 Ω = 33 Ω.

12 questions · Seed 58 · 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 20 Ω and 24 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 20 Ω, R₂ = 24 Ω · R_eq = R₁ + R₂ = ?
2. Two resistors of 6 Ω and 6 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 6 Ω, R₂ = 6 Ω · R_eq = R₁ + R₂ = ?
3. Two resistors of 45 Ω and 90 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 45 Ω ∥ 90 Ω · 1/R_eq = 1/45 + 1/90
4. Two resistors of 3 Ω and 5 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 3 Ω, R₂ = 5 Ω · R_eq = R₁ + R₂ = ?
5. Two resistors of 75 Ω and 150 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 75 Ω ∥ 150 Ω · 1/R_eq = 1/75 + 1/150
6. Two resistors of 6 Ω and 30 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 6 Ω ∥ 30 Ω · 1/R_eq = 1/6 + 1/30
7. Two resistors of 11 Ω and 18 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 11 Ω, R₂ = 18 Ω · R_eq = R₁ + R₂ = ?
8. Two resistors of 18 Ω and 36 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 18 Ω ∥ 36 Ω · 1/R_eq = 1/18 + 1/36
9. Two resistors of 30 Ω and 120 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 30 Ω ∥ 120 Ω · 1/R_eq = 1/30 + 1/120
10. Two resistors of 36 Ω and 180 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 36 Ω ∥ 180 Ω · 1/R_eq = 1/36 + 1/180
11. Two resistors of 24 Ω and 17 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 24 Ω, R₂ = 17 Ω · R_eq = R₁ + R₂ = ?
12. Two resistors of 18 Ω and 15 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 18 Ω, R₂ = 15 Ω · R_eq = R₁ + R₂ = ?

12 questions · Seed 58 · 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 20 Ω and 24 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
44 Ω
In a series circuit, resistances add directly: R_eq = 20 Ω + 24 Ω = 44 Ω.
2. Two resistors of 6 Ω and 6 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
12 Ω
In a series circuit, resistances add directly: R_eq = 6 Ω + 6 Ω = 12 Ω.
3. Two resistors of 45 Ω and 90 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
30 Ω
For two parallel resistors, R_eq = (45 × 90) ÷ (45 + 90) = 4050 ÷ 135 = 30 Ω.
4. Two resistors of 3 Ω and 5 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
8 Ω
In a series circuit, resistances add directly: R_eq = 3 Ω + 5 Ω = 8 Ω.
5. Two resistors of 75 Ω and 150 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
50 Ω
For two parallel resistors, R_eq = (75 × 150) ÷ (75 + 150) = 11250 ÷ 225 = 50 Ω.
6. Two resistors of 6 Ω and 30 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
5 Ω
For two parallel resistors, R_eq = (6 × 30) ÷ (6 + 30) = 180 ÷ 36 = 5 Ω.
7. Two resistors of 11 Ω and 18 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
29 Ω
In a series circuit, resistances add directly: R_eq = 11 Ω + 18 Ω = 29 Ω.
8. Two resistors of 18 Ω and 36 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
12 Ω
For two parallel resistors, R_eq = (18 × 36) ÷ (18 + 36) = 648 ÷ 54 = 12 Ω.
9. Two resistors of 30 Ω and 120 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
24 Ω
For two parallel resistors, R_eq = (30 × 120) ÷ (30 + 120) = 3600 ÷ 150 = 24 Ω.
10. Two resistors of 36 Ω and 180 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
30 Ω
For two parallel resistors, R_eq = (36 × 180) ÷ (36 + 180) = 6480 ÷ 216 = 30 Ω.
11. Two resistors of 24 Ω and 17 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
41 Ω
In a series circuit, resistances add directly: R_eq = 24 Ω + 17 Ω = 41 Ω.
12. Two resistors of 18 Ω and 15 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
33 Ω
In a series circuit, resistances add directly: R_eq = 18 Ω + 15 Ω = 33 Ω.

12 questions · Seed 58 · Age guidance, not curriculum certification