ScienceAges 10-12

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 10-12

Series & parallel resistor networks

Take your time. Show your thinking.

1. 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
2. Two resistors of 40 Ω and 40 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 40 Ω ∥ 40 Ω · 1/R_eq = 1/40 + 1/40
3. 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
4. Two resistors of 60 Ω and 120 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 60 Ω ∥ 120 Ω · 1/R_eq = 1/60 + 1/120
5. Two resistors of 32 Ω and 96 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 32 Ω ∥ 96 Ω · 1/R_eq = 1/32 + 1/96
6. Two resistors of 20 Ω and 20 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 20 Ω ∥ 20 Ω · 1/R_eq = 1/20 + 1/20
7. 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
8. Two resistors of 17 Ω and 3 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 17 Ω, R₂ = 3 Ω · R_eq = R₁ + R₂ = ?
9. 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
10. 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
11. Two resistors of 60 Ω and 60 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 60 Ω ∥ 60 Ω · 1/R_eq = 1/60 + 1/60
12. Two resistors of 4 Ω and 9 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 4 Ω, R₂ = 9 Ω · R_eq = R₁ + R₂ = ?

12 questions · Seed 42 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 10-12

Series & parallel resistor networks

Answers and reasoning. Review before teaching.

1. 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.
2. Two resistors of 40 Ω and 40 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
20 Ω
For two parallel resistors, R_eq = (40 × 40) ÷ (40 + 40) = 1600 ÷ 80 = 20 Ω.
3. 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.
4. Two resistors of 60 Ω and 120 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
40 Ω
For two parallel resistors, R_eq = (60 × 120) ÷ (60 + 120) = 7200 ÷ 180 = 40 Ω.
5. Two resistors of 32 Ω and 96 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
24 Ω
For two parallel resistors, R_eq = (32 × 96) ÷ (32 + 96) = 3072 ÷ 128 = 24 Ω.
6. Two resistors of 20 Ω and 20 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
10 Ω
For two parallel resistors, R_eq = (20 × 20) ÷ (20 + 20) = 400 ÷ 40 = 10 Ω.
7. 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.
8. Two resistors of 17 Ω and 3 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
20 Ω
In a series circuit, resistances add directly: R_eq = 17 Ω + 3 Ω = 20 Ω.
9. 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.
10. 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.
11. Two resistors of 60 Ω and 60 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
30 Ω
For two parallel resistors, R_eq = (60 × 60) ÷ (60 + 60) = 3600 ÷ 120 = 30 Ω.
12. Two resistors of 4 Ω and 9 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
13 Ω
In a series circuit, resistances add directly: R_eq = 4 Ω + 9 Ω = 13 Ω.

12 questions · Seed 42 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 10-12

Series & parallel resistor networks

Take your time. Show your thinking.

1. 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
2. Two resistors of 40 Ω and 40 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 40 Ω ∥ 40 Ω · 1/R_eq = 1/40 + 1/40
3. 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
4. Two resistors of 60 Ω and 120 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 60 Ω ∥ 120 Ω · 1/R_eq = 1/60 + 1/120
5. Two resistors of 32 Ω and 96 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 32 Ω ∥ 96 Ω · 1/R_eq = 1/32 + 1/96
6. Two resistors of 20 Ω and 20 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 20 Ω ∥ 20 Ω · 1/R_eq = 1/20 + 1/20
7. 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
8. Two resistors of 17 Ω and 3 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 17 Ω, R₂ = 3 Ω · R_eq = R₁ + R₂ = ?
9. 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
10. 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
11. Two resistors of 60 Ω and 60 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 60 Ω ∥ 60 Ω · 1/R_eq = 1/60 + 1/60
12. Two resistors of 4 Ω and 9 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 4 Ω, R₂ = 9 Ω · R_eq = R₁ + R₂ = ?

12 questions · Seed 42 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 10-12

Series & parallel resistor networks

Answers and reasoning. Review before teaching.

1. 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.
2. Two resistors of 40 Ω and 40 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
20 Ω
For two parallel resistors, R_eq = (40 × 40) ÷ (40 + 40) = 1600 ÷ 80 = 20 Ω.
3. 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.
4. Two resistors of 60 Ω and 120 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
40 Ω
For two parallel resistors, R_eq = (60 × 120) ÷ (60 + 120) = 7200 ÷ 180 = 40 Ω.
5. Two resistors of 32 Ω and 96 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
24 Ω
For two parallel resistors, R_eq = (32 × 96) ÷ (32 + 96) = 3072 ÷ 128 = 24 Ω.
6. Two resistors of 20 Ω and 20 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
10 Ω
For two parallel resistors, R_eq = (20 × 20) ÷ (20 + 20) = 400 ÷ 40 = 10 Ω.
7. 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.
8. Two resistors of 17 Ω and 3 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
20 Ω
In a series circuit, resistances add directly: R_eq = 17 Ω + 3 Ω = 20 Ω.
9. 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.
10. 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.
11. Two resistors of 60 Ω and 60 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
30 Ω
For two parallel resistors, R_eq = (60 × 60) ÷ (60 + 60) = 3600 ÷ 120 = 30 Ω.
12. Two resistors of 4 Ω and 9 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
13 Ω
In a series circuit, resistances add directly: R_eq = 4 Ω + 9 Ω = 13 Ω.

12 questions · Seed 42 · Age guidance, not curriculum certification