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 6 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 15 Ω, R₂ = 6 Ω · R_eq = R₁ + R₂ = ?
2. Two resistors of 6 Ω and 8 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 6 Ω, R₂ = 8 Ω · R_eq = R₁ + R₂ = ?
3. Two resistors of 3 Ω and 6 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 3 Ω ∥ 6 Ω · 1/R_eq = 1/3 + 1/6
4. Two resistors of 10 Ω and 17 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 10 Ω, R₂ = 17 Ω · R_eq = R₁ + R₂ = ?
5. Two resistors of 5 Ω and 15 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 5 Ω, R₂ = 15 Ω · R_eq = R₁ + R₂ = ?
6. Two resistors of 30 Ω and 30 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 30 Ω ∥ 30 Ω · 1/R_eq = 1/30 + 1/30
7. Two resistors of 20 Ω and 20 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 20 Ω, R₂ = 20 Ω · R_eq = R₁ + R₂ = ?
8. Two resistors of 8 Ω and 14 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 8 Ω, R₂ = 14 Ω · R_eq = R₁ + R₂ = ?
9. Two resistors of 19 Ω and 14 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 19 Ω, R₂ = 14 Ω · R_eq = R₁ + R₂ = ?
10. 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
11. Two resistors of 30 Ω and 60 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 30 Ω ∥ 60 Ω · 1/R_eq = 1/30 + 1/60
12. Two resistors of 5 Ω and 20 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 5 Ω ∥ 20 Ω · 1/R_eq = 1/5 + 1/20

12 questions · Seed 50 · 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 6 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
21 Ω
In a series circuit, resistances add directly: R_eq = 15 Ω + 6 Ω = 21 Ω.
2. Two resistors of 6 Ω and 8 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
14 Ω
In a series circuit, resistances add directly: R_eq = 6 Ω + 8 Ω = 14 Ω.
3. Two resistors of 3 Ω and 6 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
2 Ω
For two parallel resistors, R_eq = (3 × 6) ÷ (3 + 6) = 18 ÷ 9 = 2 Ω.
4. Two resistors of 10 Ω and 17 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
27 Ω
In a series circuit, resistances add directly: R_eq = 10 Ω + 17 Ω = 27 Ω.
5. Two resistors of 5 Ω and 15 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
20 Ω
In a series circuit, resistances add directly: R_eq = 5 Ω + 15 Ω = 20 Ω.
6. Two resistors of 30 Ω and 30 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
15 Ω
For two parallel resistors, R_eq = (30 × 30) ÷ (30 + 30) = 900 ÷ 60 = 15 Ω.
7. Two resistors of 20 Ω and 20 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
40 Ω
In a series circuit, resistances add directly: R_eq = 20 Ω + 20 Ω = 40 Ω.
8. Two resistors of 8 Ω and 14 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
22 Ω
In a series circuit, resistances add directly: R_eq = 8 Ω + 14 Ω = 22 Ω.
9. Two resistors of 19 Ω and 14 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
33 Ω
In a series circuit, resistances add directly: R_eq = 19 Ω + 14 Ω = 33 Ω.
10. 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.
11. Two resistors of 30 Ω and 60 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
20 Ω
For two parallel resistors, R_eq = (30 × 60) ÷ (30 + 60) = 1800 ÷ 90 = 20 Ω.
12. Two resistors of 5 Ω and 20 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
4 Ω
For two parallel resistors, R_eq = (5 × 20) ÷ (5 + 20) = 100 ÷ 25 = 4 Ω.

12 questions · Seed 50 · 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 6 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 15 Ω, R₂ = 6 Ω · R_eq = R₁ + R₂ = ?
2. Two resistors of 6 Ω and 8 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 6 Ω, R₂ = 8 Ω · R_eq = R₁ + R₂ = ?
3. Two resistors of 3 Ω and 6 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 3 Ω ∥ 6 Ω · 1/R_eq = 1/3 + 1/6
4. Two resistors of 10 Ω and 17 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 10 Ω, R₂ = 17 Ω · R_eq = R₁ + R₂ = ?
5. Two resistors of 5 Ω and 15 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 5 Ω, R₂ = 15 Ω · R_eq = R₁ + R₂ = ?
6. Two resistors of 30 Ω and 30 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 30 Ω ∥ 30 Ω · 1/R_eq = 1/30 + 1/30
7. Two resistors of 20 Ω and 20 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 20 Ω, R₂ = 20 Ω · R_eq = R₁ + R₂ = ?
8. Two resistors of 8 Ω and 14 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 8 Ω, R₂ = 14 Ω · R_eq = R₁ + R₂ = ?
9. Two resistors of 19 Ω and 14 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 19 Ω, R₂ = 14 Ω · R_eq = R₁ + R₂ = ?
10. 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
11. Two resistors of 30 Ω and 60 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 30 Ω ∥ 60 Ω · 1/R_eq = 1/30 + 1/60
12. Two resistors of 5 Ω and 20 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 5 Ω ∥ 20 Ω · 1/R_eq = 1/5 + 1/20

12 questions · Seed 50 · 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 6 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
21 Ω
In a series circuit, resistances add directly: R_eq = 15 Ω + 6 Ω = 21 Ω.
2. Two resistors of 6 Ω and 8 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
14 Ω
In a series circuit, resistances add directly: R_eq = 6 Ω + 8 Ω = 14 Ω.
3. Two resistors of 3 Ω and 6 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
2 Ω
For two parallel resistors, R_eq = (3 × 6) ÷ (3 + 6) = 18 ÷ 9 = 2 Ω.
4. Two resistors of 10 Ω and 17 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
27 Ω
In a series circuit, resistances add directly: R_eq = 10 Ω + 17 Ω = 27 Ω.
5. Two resistors of 5 Ω and 15 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
20 Ω
In a series circuit, resistances add directly: R_eq = 5 Ω + 15 Ω = 20 Ω.
6. Two resistors of 30 Ω and 30 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
15 Ω
For two parallel resistors, R_eq = (30 × 30) ÷ (30 + 30) = 900 ÷ 60 = 15 Ω.
7. Two resistors of 20 Ω and 20 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
40 Ω
In a series circuit, resistances add directly: R_eq = 20 Ω + 20 Ω = 40 Ω.
8. Two resistors of 8 Ω and 14 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
22 Ω
In a series circuit, resistances add directly: R_eq = 8 Ω + 14 Ω = 22 Ω.
9. Two resistors of 19 Ω and 14 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
33 Ω
In a series circuit, resistances add directly: R_eq = 19 Ω + 14 Ω = 33 Ω.
10. 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.
11. Two resistors of 30 Ω and 60 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
20 Ω
For two parallel resistors, R_eq = (30 × 60) ÷ (30 + 60) = 1800 ÷ 90 = 20 Ω.
12. Two resistors of 5 Ω and 20 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
4 Ω
For two parallel resistors, R_eq = (5 × 20) ÷ (5 + 20) = 100 ÷ 25 = 4 Ω.

12 questions · Seed 50 · Age guidance, not curriculum certification