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 19 Ω and 14 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 19 Ω, R₂ = 14 Ω · R_eq = R₁ + R₂ = ?
2. Two resistors of 16 Ω and 21 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 16 Ω, R₂ = 21 Ω · R_eq = R₁ + R₂ = ?
3. Two resistors of 40 Ω and 120 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 40 Ω ∥ 120 Ω · 1/R_eq = 1/40 + 1/120
4. Two resistors of 30 Ω and 150 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 30 Ω ∥ 150 Ω · 1/R_eq = 1/30 + 1/150
5. Two resistors of 4 Ω and 11 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 4 Ω, R₂ = 11 Ω · R_eq = R₁ + R₂ = ?
6. Two resistors of 15 Ω and 60 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 15 Ω ∥ 60 Ω · 1/R_eq = 1/15 + 1/60
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 11 Ω and 2 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 11 Ω, R₂ = 2 Ω · R_eq = R₁ + R₂ = ?
9. Two resistors of 25 Ω and 9 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 25 Ω, R₂ = 9 Ω · R_eq = R₁ + R₂ = ?
10. Two resistors of 25 Ω and 100 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 25 Ω ∥ 100 Ω · 1/R_eq = 1/25 + 1/100
11. 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
12. Two resistors of 4 Ω and 8 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 4 Ω, R₂ = 8 Ω · R_eq = R₁ + R₂ = ?

12 questions · Seed 49 · 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 19 Ω and 14 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
33 Ω
In a series circuit, resistances add directly: R_eq = 19 Ω + 14 Ω = 33 Ω.
2. Two resistors of 16 Ω and 21 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
37 Ω
In a series circuit, resistances add directly: R_eq = 16 Ω + 21 Ω = 37 Ω.
3. Two resistors of 40 Ω and 120 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
30 Ω
For two parallel resistors, R_eq = (40 × 120) ÷ (40 + 120) = 4800 ÷ 160 = 30 Ω.
4. Two resistors of 30 Ω and 150 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
25 Ω
For two parallel resistors, R_eq = (30 × 150) ÷ (30 + 150) = 4500 ÷ 180 = 25 Ω.
5. Two resistors of 4 Ω and 11 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
15 Ω
In a series circuit, resistances add directly: R_eq = 4 Ω + 11 Ω = 15 Ω.
6. Two resistors of 15 Ω and 60 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
12 Ω
For two parallel resistors, R_eq = (15 × 60) ÷ (15 + 60) = 900 ÷ 75 = 12 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 11 Ω and 2 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
13 Ω
In a series circuit, resistances add directly: R_eq = 11 Ω + 2 Ω = 13 Ω.
9. Two resistors of 25 Ω and 9 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
34 Ω
In a series circuit, resistances add directly: R_eq = 25 Ω + 9 Ω = 34 Ω.
10. Two resistors of 25 Ω and 100 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
20 Ω
For two parallel resistors, R_eq = (25 × 100) ÷ (25 + 100) = 2500 ÷ 125 = 20 Ω.
11. 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.
12. Two resistors of 4 Ω and 8 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
12 Ω
In a series circuit, resistances add directly: R_eq = 4 Ω + 8 Ω = 12 Ω.

12 questions · Seed 49 · 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 19 Ω and 14 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 19 Ω, R₂ = 14 Ω · R_eq = R₁ + R₂ = ?
2. Two resistors of 16 Ω and 21 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 16 Ω, R₂ = 21 Ω · R_eq = R₁ + R₂ = ?
3. Two resistors of 40 Ω and 120 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 40 Ω ∥ 120 Ω · 1/R_eq = 1/40 + 1/120
4. Two resistors of 30 Ω and 150 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 30 Ω ∥ 150 Ω · 1/R_eq = 1/30 + 1/150
5. Two resistors of 4 Ω and 11 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 4 Ω, R₂ = 11 Ω · R_eq = R₁ + R₂ = ?
6. Two resistors of 15 Ω and 60 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 15 Ω ∥ 60 Ω · 1/R_eq = 1/15 + 1/60
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 11 Ω and 2 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 11 Ω, R₂ = 2 Ω · R_eq = R₁ + R₂ = ?
9. Two resistors of 25 Ω and 9 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 25 Ω, R₂ = 9 Ω · R_eq = R₁ + R₂ = ?
10. Two resistors of 25 Ω and 100 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 25 Ω ∥ 100 Ω · 1/R_eq = 1/25 + 1/100
11. 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
12. Two resistors of 4 Ω and 8 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 4 Ω, R₂ = 8 Ω · R_eq = R₁ + R₂ = ?

12 questions · Seed 49 · 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 19 Ω and 14 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
33 Ω
In a series circuit, resistances add directly: R_eq = 19 Ω + 14 Ω = 33 Ω.
2. Two resistors of 16 Ω and 21 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
37 Ω
In a series circuit, resistances add directly: R_eq = 16 Ω + 21 Ω = 37 Ω.
3. Two resistors of 40 Ω and 120 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
30 Ω
For two parallel resistors, R_eq = (40 × 120) ÷ (40 + 120) = 4800 ÷ 160 = 30 Ω.
4. Two resistors of 30 Ω and 150 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
25 Ω
For two parallel resistors, R_eq = (30 × 150) ÷ (30 + 150) = 4500 ÷ 180 = 25 Ω.
5. Two resistors of 4 Ω and 11 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
15 Ω
In a series circuit, resistances add directly: R_eq = 4 Ω + 11 Ω = 15 Ω.
6. Two resistors of 15 Ω and 60 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
12 Ω
For two parallel resistors, R_eq = (15 × 60) ÷ (15 + 60) = 900 ÷ 75 = 12 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 11 Ω and 2 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
13 Ω
In a series circuit, resistances add directly: R_eq = 11 Ω + 2 Ω = 13 Ω.
9. Two resistors of 25 Ω and 9 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
34 Ω
In a series circuit, resistances add directly: R_eq = 25 Ω + 9 Ω = 34 Ω.
10. Two resistors of 25 Ω and 100 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
20 Ω
For two parallel resistors, R_eq = (25 × 100) ÷ (25 + 100) = 2500 ÷ 125 = 20 Ω.
11. 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.
12. Two resistors of 4 Ω and 8 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
12 Ω
In a series circuit, resistances add directly: R_eq = 4 Ω + 8 Ω = 12 Ω.

12 questions · Seed 49 · Age guidance, not curriculum certification