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 8 Ω and 2 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 8 Ω, R₂ = 2 Ω · R_eq = R₁ + R₂ = ?
2. Two resistors of 6 Ω and 15 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 6 Ω, R₂ = 15 Ω · R_eq = R₁ + R₂ = ?
3. Two resistors of 12 Ω and 8 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 12 Ω, R₂ = 8 Ω · R_eq = R₁ + R₂ = ?
4. Two resistors of 4 Ω and 20 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 4 Ω, R₂ = 20 Ω · R_eq = R₁ + R₂ = ?
5. Two resistors of 24 Ω and 14 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 24 Ω, R₂ = 14 Ω · R_eq = R₁ + R₂ = ?
6. 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
7. 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
8. Two resistors of 11 Ω and 24 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 11 Ω, R₂ = 24 Ω · R_eq = R₁ + R₂ = ?
9. Two resistors of 18 Ω and 25 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 18 Ω, R₂ = 25 Ω · R_eq = R₁ + R₂ = ?
10. Two resistors of 9 Ω and 3 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 9 Ω, R₂ = 3 Ω · R_eq = R₁ + R₂ = ?
11. 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
12. Two resistors of 6 Ω and 6 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 6 Ω, R₂ = 6 Ω · R_eq = R₁ + R₂ = ?

12 questions · Seed 52 · 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 8 Ω and 2 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
10 Ω
In a series circuit, resistances add directly: R_eq = 8 Ω + 2 Ω = 10 Ω.
2. Two resistors of 6 Ω and 15 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
21 Ω
In a series circuit, resistances add directly: R_eq = 6 Ω + 15 Ω = 21 Ω.
3. Two resistors of 12 Ω and 8 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
20 Ω
In a series circuit, resistances add directly: R_eq = 12 Ω + 8 Ω = 20 Ω.
4. Two resistors of 4 Ω and 20 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
24 Ω
In a series circuit, resistances add directly: R_eq = 4 Ω + 20 Ω = 24 Ω.
5. Two resistors of 24 Ω and 14 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
38 Ω
In a series circuit, resistances add directly: R_eq = 24 Ω + 14 Ω = 38 Ω.
6. 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.
7. 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.
8. Two resistors of 11 Ω and 24 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
35 Ω
In a series circuit, resistances add directly: R_eq = 11 Ω + 24 Ω = 35 Ω.
9. Two resistors of 18 Ω and 25 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
43 Ω
In a series circuit, resistances add directly: R_eq = 18 Ω + 25 Ω = 43 Ω.
10. Two resistors of 9 Ω and 3 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
12 Ω
In a series circuit, resistances add directly: R_eq = 9 Ω + 3 Ω = 12 Ω.
11. 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.
12. Two resistors of 6 Ω and 6 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
12 Ω
In a series circuit, resistances add directly: R_eq = 6 Ω + 6 Ω = 12 Ω.

12 questions · Seed 52 · 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 8 Ω and 2 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 8 Ω, R₂ = 2 Ω · R_eq = R₁ + R₂ = ?
2. Two resistors of 6 Ω and 15 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 6 Ω, R₂ = 15 Ω · R_eq = R₁ + R₂ = ?
3. Two resistors of 12 Ω and 8 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 12 Ω, R₂ = 8 Ω · R_eq = R₁ + R₂ = ?
4. Two resistors of 4 Ω and 20 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 4 Ω, R₂ = 20 Ω · R_eq = R₁ + R₂ = ?
5. Two resistors of 24 Ω and 14 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 24 Ω, R₂ = 14 Ω · R_eq = R₁ + R₂ = ?
6. 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
7. 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
8. Two resistors of 11 Ω and 24 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 11 Ω, R₂ = 24 Ω · R_eq = R₁ + R₂ = ?
9. Two resistors of 18 Ω and 25 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 18 Ω, R₂ = 25 Ω · R_eq = R₁ + R₂ = ?
10. Two resistors of 9 Ω and 3 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 9 Ω, R₂ = 3 Ω · R_eq = R₁ + R₂ = ?
11. 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
12. Two resistors of 6 Ω and 6 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 6 Ω, R₂ = 6 Ω · R_eq = R₁ + R₂ = ?

12 questions · Seed 52 · 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 8 Ω and 2 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
10 Ω
In a series circuit, resistances add directly: R_eq = 8 Ω + 2 Ω = 10 Ω.
2. Two resistors of 6 Ω and 15 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
21 Ω
In a series circuit, resistances add directly: R_eq = 6 Ω + 15 Ω = 21 Ω.
3. Two resistors of 12 Ω and 8 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
20 Ω
In a series circuit, resistances add directly: R_eq = 12 Ω + 8 Ω = 20 Ω.
4. Two resistors of 4 Ω and 20 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
24 Ω
In a series circuit, resistances add directly: R_eq = 4 Ω + 20 Ω = 24 Ω.
5. Two resistors of 24 Ω and 14 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
38 Ω
In a series circuit, resistances add directly: R_eq = 24 Ω + 14 Ω = 38 Ω.
6. 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.
7. 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.
8. Two resistors of 11 Ω and 24 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
35 Ω
In a series circuit, resistances add directly: R_eq = 11 Ω + 24 Ω = 35 Ω.
9. Two resistors of 18 Ω and 25 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
43 Ω
In a series circuit, resistances add directly: R_eq = 18 Ω + 25 Ω = 43 Ω.
10. Two resistors of 9 Ω and 3 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
12 Ω
In a series circuit, resistances add directly: R_eq = 9 Ω + 3 Ω = 12 Ω.
11. 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.
12. Two resistors of 6 Ω and 6 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
12 Ω
In a series circuit, resistances add directly: R_eq = 6 Ω + 6 Ω = 12 Ω.

12 questions · Seed 52 · Age guidance, not curriculum certification