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 15 Ω and 19 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 15 Ω, R₂ = 19 Ω · R_eq = R₁ + R₂ = ?
2. 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
3. Two resistors of 21 Ω and 9 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 21 Ω, R₂ = 9 Ω · R_eq = R₁ + R₂ = ?
4. Two resistors of 50 Ω and 50 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 50 Ω ∥ 50 Ω · 1/R_eq = 1/50 + 1/50
5. Two resistors of 10 Ω and 10 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 10 Ω ∥ 10 Ω · 1/R_eq = 1/10 + 1/10
6. Two resistors of 90 Ω and 180 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 90 Ω ∥ 180 Ω · 1/R_eq = 1/90 + 1/180
7. 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
8. Two resistors of 12 Ω and 24 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 12 Ω ∥ 24 Ω · 1/R_eq = 1/12 + 1/24
9. Two resistors of 8 Ω and 20 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 8 Ω, R₂ = 20 Ω · R_eq = R₁ + R₂ = ?
10. 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
11. Two resistors of 18 Ω and 4 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 18 Ω, R₂ = 4 Ω · R_eq = R₁ + R₂ = ?
12. Two resistors of 4 Ω and 12 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 4 Ω ∥ 12 Ω · 1/R_eq = 1/4 + 1/12

12 questions · Seed 60 · 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 15 Ω and 19 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
34 Ω
In a series circuit, resistances add directly: R_eq = 15 Ω + 19 Ω = 34 Ω.
2. 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.
3. Two resistors of 21 Ω and 9 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
30 Ω
In a series circuit, resistances add directly: R_eq = 21 Ω + 9 Ω = 30 Ω.
4. Two resistors of 50 Ω and 50 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
25 Ω
For two parallel resistors, R_eq = (50 × 50) ÷ (50 + 50) = 2500 ÷ 100 = 25 Ω.
5. Two resistors of 10 Ω and 10 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
5 Ω
For two parallel resistors, R_eq = (10 × 10) ÷ (10 + 10) = 100 ÷ 20 = 5 Ω.
6. Two resistors of 90 Ω and 180 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
60 Ω
For two parallel resistors, R_eq = (90 × 180) ÷ (90 + 180) = 16200 ÷ 270 = 60 Ω.
7. 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.
8. Two resistors of 12 Ω and 24 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
8 Ω
For two parallel resistors, R_eq = (12 × 24) ÷ (12 + 24) = 288 ÷ 36 = 8 Ω.
9. Two resistors of 8 Ω and 20 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
28 Ω
In a series circuit, resistances add directly: R_eq = 8 Ω + 20 Ω = 28 Ω.
10. 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.
11. Two resistors of 18 Ω and 4 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
22 Ω
In a series circuit, resistances add directly: R_eq = 18 Ω + 4 Ω = 22 Ω.
12. Two resistors of 4 Ω and 12 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
3 Ω
For two parallel resistors, R_eq = (4 × 12) ÷ (4 + 12) = 48 ÷ 16 = 3 Ω.

12 questions · Seed 60 · 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 15 Ω and 19 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 15 Ω, R₂ = 19 Ω · R_eq = R₁ + R₂ = ?
2. 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
3. Two resistors of 21 Ω and 9 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 21 Ω, R₂ = 9 Ω · R_eq = R₁ + R₂ = ?
4. Two resistors of 50 Ω and 50 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 50 Ω ∥ 50 Ω · 1/R_eq = 1/50 + 1/50
5. Two resistors of 10 Ω and 10 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 10 Ω ∥ 10 Ω · 1/R_eq = 1/10 + 1/10
6. Two resistors of 90 Ω and 180 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 90 Ω ∥ 180 Ω · 1/R_eq = 1/90 + 1/180
7. 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
8. Two resistors of 12 Ω and 24 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 12 Ω ∥ 24 Ω · 1/R_eq = 1/12 + 1/24
9. Two resistors of 8 Ω and 20 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 8 Ω, R₂ = 20 Ω · R_eq = R₁ + R₂ = ?
10. 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
11. Two resistors of 18 Ω and 4 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 18 Ω, R₂ = 4 Ω · R_eq = R₁ + R₂ = ?
12. Two resistors of 4 Ω and 12 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 4 Ω ∥ 12 Ω · 1/R_eq = 1/4 + 1/12

12 questions · Seed 60 · 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 15 Ω and 19 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
34 Ω
In a series circuit, resistances add directly: R_eq = 15 Ω + 19 Ω = 34 Ω.
2. 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.
3. Two resistors of 21 Ω and 9 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
30 Ω
In a series circuit, resistances add directly: R_eq = 21 Ω + 9 Ω = 30 Ω.
4. Two resistors of 50 Ω and 50 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
25 Ω
For two parallel resistors, R_eq = (50 × 50) ÷ (50 + 50) = 2500 ÷ 100 = 25 Ω.
5. Two resistors of 10 Ω and 10 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
5 Ω
For two parallel resistors, R_eq = (10 × 10) ÷ (10 + 10) = 100 ÷ 20 = 5 Ω.
6. Two resistors of 90 Ω and 180 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
60 Ω
For two parallel resistors, R_eq = (90 × 180) ÷ (90 + 180) = 16200 ÷ 270 = 60 Ω.
7. 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.
8. Two resistors of 12 Ω and 24 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
8 Ω
For two parallel resistors, R_eq = (12 × 24) ÷ (12 + 24) = 288 ÷ 36 = 8 Ω.
9. Two resistors of 8 Ω and 20 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
28 Ω
In a series circuit, resistances add directly: R_eq = 8 Ω + 20 Ω = 28 Ω.
10. 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.
11. Two resistors of 18 Ω and 4 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
22 Ω
In a series circuit, resistances add directly: R_eq = 18 Ω + 4 Ω = 22 Ω.
12. Two resistors of 4 Ω and 12 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
3 Ω
For two parallel resistors, R_eq = (4 × 12) ÷ (4 + 12) = 48 ÷ 16 = 3 Ω.

12 questions · Seed 60 · Age guidance, not curriculum certification