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 23 Ω and 6 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 23 Ω, R₂ = 6 Ω · R_eq = R₁ + R₂ = ?
2. Two resistors of 23 Ω and 8 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 23 Ω, R₂ = 8 Ω · R_eq = R₁ + R₂ = ?
3. Two resistors of 24 Ω and 72 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 24 Ω ∥ 72 Ω · 1/R_eq = 1/24 + 1/72
4. Two resistors of 20 Ω and 23 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 20 Ω, R₂ = 23 Ω · R_eq = R₁ + R₂ = ?
5. Two resistors of 11 Ω and 3 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 11 Ω, R₂ = 3 Ω · R_eq = R₁ + R₂ = ?
6. Two resistors of 23 Ω and 14 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 23 Ω, R₂ = 14 Ω · R_eq = R₁ + R₂ = ?
7. Two resistors of 18 Ω and 36 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 18 Ω ∥ 36 Ω · 1/R_eq = 1/18 + 1/36
8. Two resistors of 13 Ω and 25 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 13 Ω, R₂ = 25 Ω · R_eq = R₁ + R₂ = ?
9. 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
10. 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
11. 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
12. Two resistors of 24 Ω and 19 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 24 Ω, R₂ = 19 Ω · R_eq = R₁ + R₂ = ?

12 questions · Seed 43 · 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 23 Ω and 6 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
29 Ω
In a series circuit, resistances add directly: R_eq = 23 Ω + 6 Ω = 29 Ω.
2. Two resistors of 23 Ω and 8 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
31 Ω
In a series circuit, resistances add directly: R_eq = 23 Ω + 8 Ω = 31 Ω.
3. Two resistors of 24 Ω and 72 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
18 Ω
For two parallel resistors, R_eq = (24 × 72) ÷ (24 + 72) = 1728 ÷ 96 = 18 Ω.
4. Two resistors of 20 Ω and 23 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
43 Ω
In a series circuit, resistances add directly: R_eq = 20 Ω + 23 Ω = 43 Ω.
5. Two resistors of 11 Ω and 3 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
14 Ω
In a series circuit, resistances add directly: R_eq = 11 Ω + 3 Ω = 14 Ω.
6. Two resistors of 23 Ω and 14 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
37 Ω
In a series circuit, resistances add directly: R_eq = 23 Ω + 14 Ω = 37 Ω.
7. Two resistors of 18 Ω and 36 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
12 Ω
For two parallel resistors, R_eq = (18 × 36) ÷ (18 + 36) = 648 ÷ 54 = 12 Ω.
8. Two resistors of 13 Ω and 25 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
38 Ω
In a series circuit, resistances add directly: R_eq = 13 Ω + 25 Ω = 38 Ω.
9. 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.
10. 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.
11. 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.
12. Two resistors of 24 Ω and 19 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
43 Ω
In a series circuit, resistances add directly: R_eq = 24 Ω + 19 Ω = 43 Ω.

12 questions · Seed 43 · 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 23 Ω and 6 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 23 Ω, R₂ = 6 Ω · R_eq = R₁ + R₂ = ?
2. Two resistors of 23 Ω and 8 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 23 Ω, R₂ = 8 Ω · R_eq = R₁ + R₂ = ?
3. Two resistors of 24 Ω and 72 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 24 Ω ∥ 72 Ω · 1/R_eq = 1/24 + 1/72
4. Two resistors of 20 Ω and 23 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 20 Ω, R₂ = 23 Ω · R_eq = R₁ + R₂ = ?
5. Two resistors of 11 Ω and 3 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 11 Ω, R₂ = 3 Ω · R_eq = R₁ + R₂ = ?
6. Two resistors of 23 Ω and 14 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 23 Ω, R₂ = 14 Ω · R_eq = R₁ + R₂ = ?
7. Two resistors of 18 Ω and 36 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 18 Ω ∥ 36 Ω · 1/R_eq = 1/18 + 1/36
8. Two resistors of 13 Ω and 25 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 13 Ω, R₂ = 25 Ω · R_eq = R₁ + R₂ = ?
9. 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
10. 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
11. 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
12. Two resistors of 24 Ω and 19 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 24 Ω, R₂ = 19 Ω · R_eq = R₁ + R₂ = ?

12 questions · Seed 43 · 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 23 Ω and 6 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
29 Ω
In a series circuit, resistances add directly: R_eq = 23 Ω + 6 Ω = 29 Ω.
2. Two resistors of 23 Ω and 8 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
31 Ω
In a series circuit, resistances add directly: R_eq = 23 Ω + 8 Ω = 31 Ω.
3. Two resistors of 24 Ω and 72 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
18 Ω
For two parallel resistors, R_eq = (24 × 72) ÷ (24 + 72) = 1728 ÷ 96 = 18 Ω.
4. Two resistors of 20 Ω and 23 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
43 Ω
In a series circuit, resistances add directly: R_eq = 20 Ω + 23 Ω = 43 Ω.
5. Two resistors of 11 Ω and 3 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
14 Ω
In a series circuit, resistances add directly: R_eq = 11 Ω + 3 Ω = 14 Ω.
6. Two resistors of 23 Ω and 14 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
37 Ω
In a series circuit, resistances add directly: R_eq = 23 Ω + 14 Ω = 37 Ω.
7. Two resistors of 18 Ω and 36 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
12 Ω
For two parallel resistors, R_eq = (18 × 36) ÷ (18 + 36) = 648 ÷ 54 = 12 Ω.
8. Two resistors of 13 Ω and 25 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
38 Ω
In a series circuit, resistances add directly: R_eq = 13 Ω + 25 Ω = 38 Ω.
9. 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.
10. 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.
11. 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.
12. Two resistors of 24 Ω and 19 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
43 Ω
In a series circuit, resistances add directly: R_eq = 24 Ω + 19 Ω = 43 Ω.

12 questions · Seed 43 · Age guidance, not curriculum certification