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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Worksheet StudioPractice pack · Ages 10-12

Series & parallel resistor networks

Take your time. Show your thinking.

1. Two resistors of 25 Ω and 17 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 25 Ω, R₂ = 17 Ω · R_eq = R₁ + R₂ = ?
2. Two resistors of 4 Ω and 3 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 4 Ω, R₂ = 3 Ω · R_eq = R₁ + R₂ = ?
3. 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
4. Two resistors of 9 Ω and 18 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 9 Ω, R₂ = 18 Ω · R_eq = R₁ + R₂ = ?
5. 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
6. Two resistors of 23 Ω and 17 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 23 Ω, R₂ = 17 Ω · R_eq = R₁ + R₂ = ?
7. 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
8. Two resistors of 10 Ω and 15 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 10 Ω, R₂ = 15 Ω · R_eq = R₁ + R₂ = ?
9. 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
10. 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
11. 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
12. Two resistors of 14 Ω and 2 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 14 Ω, R₂ = 2 Ω · R_eq = R₁ + R₂ = ?

12 questions · Seed 104729 · 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 25 Ω and 17 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
42 Ω
In a series circuit, resistances add directly: R_eq = 25 Ω + 17 Ω = 42 Ω.
2. Two resistors of 4 Ω and 3 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
7 Ω
In a series circuit, resistances add directly: R_eq = 4 Ω + 3 Ω = 7 Ω.
3. 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.
4. Two resistors of 9 Ω and 18 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
27 Ω
In a series circuit, resistances add directly: R_eq = 9 Ω + 18 Ω = 27 Ω.
5. 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.
6. Two resistors of 23 Ω and 17 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
40 Ω
In a series circuit, resistances add directly: R_eq = 23 Ω + 17 Ω = 40 Ω.
7. 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.
8. Two resistors of 10 Ω and 15 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
25 Ω
In a series circuit, resistances add directly: R_eq = 10 Ω + 15 Ω = 25 Ω.
9. 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.
10. 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.
11. 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.
12. Two resistors of 14 Ω and 2 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
16 Ω
In a series circuit, resistances add directly: R_eq = 14 Ω + 2 Ω = 16 Ω.

12 questions · Seed 104729 · 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 25 Ω and 17 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 25 Ω, R₂ = 17 Ω · R_eq = R₁ + R₂ = ?
2. Two resistors of 4 Ω and 3 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 4 Ω, R₂ = 3 Ω · R_eq = R₁ + R₂ = ?
3. 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
4. Two resistors of 9 Ω and 18 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 9 Ω, R₂ = 18 Ω · R_eq = R₁ + R₂ = ?
5. 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
6. Two resistors of 23 Ω and 17 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 23 Ω, R₂ = 17 Ω · R_eq = R₁ + R₂ = ?
7. 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
8. Two resistors of 10 Ω and 15 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 10 Ω, R₂ = 15 Ω · R_eq = R₁ + R₂ = ?
9. 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
10. 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
11. 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
12. Two resistors of 14 Ω and 2 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 14 Ω, R₂ = 2 Ω · R_eq = R₁ + R₂ = ?

12 questions · Seed 104729 · 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 25 Ω and 17 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
42 Ω
In a series circuit, resistances add directly: R_eq = 25 Ω + 17 Ω = 42 Ω.
2. Two resistors of 4 Ω and 3 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
7 Ω
In a series circuit, resistances add directly: R_eq = 4 Ω + 3 Ω = 7 Ω.
3. 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.
4. Two resistors of 9 Ω and 18 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
27 Ω
In a series circuit, resistances add directly: R_eq = 9 Ω + 18 Ω = 27 Ω.
5. 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.
6. Two resistors of 23 Ω and 17 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
40 Ω
In a series circuit, resistances add directly: R_eq = 23 Ω + 17 Ω = 40 Ω.
7. 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.
8. Two resistors of 10 Ω and 15 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
25 Ω
In a series circuit, resistances add directly: R_eq = 10 Ω + 15 Ω = 25 Ω.
9. 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.
10. 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.
11. 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.
12. Two resistors of 14 Ω and 2 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
16 Ω
In a series circuit, resistances add directly: R_eq = 14 Ω + 2 Ω = 16 Ω.

12 questions · Seed 104729 · Age guidance, not curriculum certification