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.

New variation Try interactive challenge Browse templates

Age band:Ages 10-12 Ages 13-15

Choose “Save as PDF” to keep a copy. Use your browser’s paper setting for A4 or Letter.

Worksheet StudioPractice pack · Ages 13-15

Series & parallel resistor networks

Take your time. Show your thinking.

1. Two resistors of 16 Ω and 10 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 16 Ω, R₂ = 10 Ω · R_eq = R₁ + R₂ = ?
2. Two resistors of 2 Ω and 17 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 2 Ω, R₂ = 17 Ω · R_eq = R₁ + R₂ = ?
3. Two resistors of 23 Ω and 18 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 23 Ω, R₂ = 18 Ω · R_eq = R₁ + R₂ = ?
4. Two resistors of 72 Ω and 144 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 72 Ω ∥ 144 Ω · 1/R_eq = 1/72 + 1/144
5. Two resistors of 23 Ω and 2 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 23 Ω, R₂ = 2 Ω · R_eq = R₁ + R₂ = ?
6. Two resistors of 9 Ω and 6 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 9 Ω, R₂ = 6 Ω · R_eq = R₁ + R₂ = ?
7. 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
8. Two resistors of 7 Ω and 18 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 7 Ω, R₂ = 18 Ω · R_eq = R₁ + R₂ = ?
9. Two resistors of 24 Ω and 120 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 24 Ω ∥ 120 Ω · 1/R_eq = 1/24 + 1/120
10. Two resistors of 9 Ω and 18 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 9 Ω ∥ 18 Ω · 1/R_eq = 1/9 + 1/18
11. Two resistors of 15 Ω and 30 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 15 Ω ∥ 30 Ω · 1/R_eq = 1/15 + 1/30
12. 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 questions · Seed 45 · 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 16 Ω and 10 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
26 Ω
In a series circuit, resistances add directly: R_eq = 16 Ω + 10 Ω = 26 Ω.
2. Two resistors of 2 Ω and 17 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
19 Ω
In a series circuit, resistances add directly: R_eq = 2 Ω + 17 Ω = 19 Ω.
3. Two resistors of 23 Ω and 18 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
41 Ω
In a series circuit, resistances add directly: R_eq = 23 Ω + 18 Ω = 41 Ω.
4. Two resistors of 72 Ω and 144 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
48 Ω
For two parallel resistors, R_eq = (72 × 144) ÷ (72 + 144) = 10368 ÷ 216 = 48 Ω.
5. Two resistors of 23 Ω and 2 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
25 Ω
In a series circuit, resistances add directly: R_eq = 23 Ω + 2 Ω = 25 Ω.
6. Two resistors of 9 Ω and 6 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
15 Ω
In a series circuit, resistances add directly: R_eq = 9 Ω + 6 Ω = 15 Ω.
7. 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.
8. Two resistors of 7 Ω and 18 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
25 Ω
In a series circuit, resistances add directly: R_eq = 7 Ω + 18 Ω = 25 Ω.
9. Two resistors of 24 Ω and 120 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
20 Ω
For two parallel resistors, R_eq = (24 × 120) ÷ (24 + 120) = 2880 ÷ 144 = 20 Ω.
10. Two resistors of 9 Ω and 18 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
6 Ω
For two parallel resistors, R_eq = (9 × 18) ÷ (9 + 18) = 162 ÷ 27 = 6 Ω.
11. Two resistors of 15 Ω and 30 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
10 Ω
For two parallel resistors, R_eq = (15 × 30) ÷ (15 + 30) = 450 ÷ 45 = 10 Ω.
12. 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 questions · Seed 45 · 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 16 Ω and 10 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 16 Ω, R₂ = 10 Ω · R_eq = R₁ + R₂ = ?
2. Two resistors of 2 Ω and 17 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 2 Ω, R₂ = 17 Ω · R_eq = R₁ + R₂ = ?
3. Two resistors of 23 Ω and 18 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 23 Ω, R₂ = 18 Ω · R_eq = R₁ + R₂ = ?
4. Two resistors of 72 Ω and 144 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 72 Ω ∥ 144 Ω · 1/R_eq = 1/72 + 1/144
5. Two resistors of 23 Ω and 2 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 23 Ω, R₂ = 2 Ω · R_eq = R₁ + R₂ = ?
6. Two resistors of 9 Ω and 6 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 9 Ω, R₂ = 6 Ω · R_eq = R₁ + R₂ = ?
7. 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
8. Two resistors of 7 Ω and 18 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 7 Ω, R₂ = 18 Ω · R_eq = R₁ + R₂ = ?
9. Two resistors of 24 Ω and 120 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 24 Ω ∥ 120 Ω · 1/R_eq = 1/24 + 1/120
10. Two resistors of 9 Ω and 18 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 9 Ω ∥ 18 Ω · 1/R_eq = 1/9 + 1/18
11. Two resistors of 15 Ω and 30 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 15 Ω ∥ 30 Ω · 1/R_eq = 1/15 + 1/30
12. 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 questions · Seed 45 · 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 16 Ω and 10 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
26 Ω
In a series circuit, resistances add directly: R_eq = 16 Ω + 10 Ω = 26 Ω.
2. Two resistors of 2 Ω and 17 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
19 Ω
In a series circuit, resistances add directly: R_eq = 2 Ω + 17 Ω = 19 Ω.
3. Two resistors of 23 Ω and 18 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
41 Ω
In a series circuit, resistances add directly: R_eq = 23 Ω + 18 Ω = 41 Ω.
4. Two resistors of 72 Ω and 144 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
48 Ω
For two parallel resistors, R_eq = (72 × 144) ÷ (72 + 144) = 10368 ÷ 216 = 48 Ω.
5. Two resistors of 23 Ω and 2 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
25 Ω
In a series circuit, resistances add directly: R_eq = 23 Ω + 2 Ω = 25 Ω.
6. Two resistors of 9 Ω and 6 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
15 Ω
In a series circuit, resistances add directly: R_eq = 9 Ω + 6 Ω = 15 Ω.
7. 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.
8. Two resistors of 7 Ω and 18 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
25 Ω
In a series circuit, resistances add directly: R_eq = 7 Ω + 18 Ω = 25 Ω.
9. Two resistors of 24 Ω and 120 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
20 Ω
For two parallel resistors, R_eq = (24 × 120) ÷ (24 + 120) = 2880 ÷ 144 = 20 Ω.
10. Two resistors of 9 Ω and 18 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
6 Ω
For two parallel resistors, R_eq = (9 × 18) ÷ (9 + 18) = 162 ÷ 27 = 6 Ω.
11. Two resistors of 15 Ω and 30 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
10 Ω
For two parallel resistors, R_eq = (15 × 30) ÷ (15 + 30) = 450 ÷ 45 = 10 Ω.
12. 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 questions · Seed 45 · Age guidance, not curriculum certification