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 25 Ω and 100 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 25 Ω ∥ 100 Ω · 1/R_eq = 1/25 + 1/100
2. 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
3. Two resistors of 22 Ω and 9 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 22 Ω, R₂ = 9 Ω · R_eq = R₁ + R₂ = ?
4. Two resistors of 3 Ω and 9 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 3 Ω, R₂ = 9 Ω · R_eq = R₁ + R₂ = ?
5. Two resistors of 10 Ω and 10 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 10 Ω ∥ 10 Ω · 1/R_eq = 1/10 + 1/10
6. 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 = ?
7. Two resistors of 4 Ω and 17 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 4 Ω, R₂ = 17 Ω · R_eq = R₁ + R₂ = ?
8. Two resistors of 7 Ω and 12 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 7 Ω, R₂ = 12 Ω · R_eq = R₁ + R₂ = ?
9. 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
10. 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
11. Two resistors of 16 Ω and 16 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 16 Ω, R₂ = 16 Ω · R_eq = R₁ + R₂ = ?
12. Two resistors of 13 Ω and 15 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 13 Ω, R₂ = 15 Ω · R_eq = R₁ + R₂ = ?

12 questions · Seed 56 · 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 100 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
20 Ω
For two parallel resistors, R_eq = (25 × 100) ÷ (25 + 100) = 2500 ÷ 125 = 20 Ω.
2. 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.
3. Two resistors of 22 Ω and 9 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
31 Ω
In a series circuit, resistances add directly: R_eq = 22 Ω + 9 Ω = 31 Ω.
4. Two resistors of 3 Ω and 9 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
12 Ω
In a series circuit, resistances add directly: R_eq = 3 Ω + 9 Ω = 12 Ω.
5. Two resistors of 10 Ω and 10 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
5 Ω
For two parallel resistors, R_eq = (10 × 10) ÷ (10 + 10) = 100 ÷ 20 = 5 Ω.
6. 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.
7. Two resistors of 4 Ω and 17 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
21 Ω
In a series circuit, resistances add directly: R_eq = 4 Ω + 17 Ω = 21 Ω.
8. Two resistors of 7 Ω and 12 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
19 Ω
In a series circuit, resistances add directly: R_eq = 7 Ω + 12 Ω = 19 Ω.
9. 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.
10. 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.
11. Two resistors of 16 Ω and 16 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
32 Ω
In a series circuit, resistances add directly: R_eq = 16 Ω + 16 Ω = 32 Ω.
12. Two resistors of 13 Ω and 15 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
28 Ω
In a series circuit, resistances add directly: R_eq = 13 Ω + 15 Ω = 28 Ω.

12 questions · Seed 56 · 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 100 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 25 Ω ∥ 100 Ω · 1/R_eq = 1/25 + 1/100
2. 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
3. Two resistors of 22 Ω and 9 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 22 Ω, R₂ = 9 Ω · R_eq = R₁ + R₂ = ?
4. Two resistors of 3 Ω and 9 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 3 Ω, R₂ = 9 Ω · R_eq = R₁ + R₂ = ?
5. Two resistors of 10 Ω and 10 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 10 Ω ∥ 10 Ω · 1/R_eq = 1/10 + 1/10
6. 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 = ?
7. Two resistors of 4 Ω and 17 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 4 Ω, R₂ = 17 Ω · R_eq = R₁ + R₂ = ?
8. Two resistors of 7 Ω and 12 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 7 Ω, R₂ = 12 Ω · R_eq = R₁ + R₂ = ?
9. 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
10. 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
11. Two resistors of 16 Ω and 16 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 16 Ω, R₂ = 16 Ω · R_eq = R₁ + R₂ = ?
12. Two resistors of 13 Ω and 15 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 13 Ω, R₂ = 15 Ω · R_eq = R₁ + R₂ = ?

12 questions · Seed 56 · 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 100 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
20 Ω
For two parallel resistors, R_eq = (25 × 100) ÷ (25 + 100) = 2500 ÷ 125 = 20 Ω.
2. 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.
3. Two resistors of 22 Ω and 9 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
31 Ω
In a series circuit, resistances add directly: R_eq = 22 Ω + 9 Ω = 31 Ω.
4. Two resistors of 3 Ω and 9 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
12 Ω
In a series circuit, resistances add directly: R_eq = 3 Ω + 9 Ω = 12 Ω.
5. Two resistors of 10 Ω and 10 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
5 Ω
For two parallel resistors, R_eq = (10 × 10) ÷ (10 + 10) = 100 ÷ 20 = 5 Ω.
6. 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.
7. Two resistors of 4 Ω and 17 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
21 Ω
In a series circuit, resistances add directly: R_eq = 4 Ω + 17 Ω = 21 Ω.
8. Two resistors of 7 Ω and 12 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
19 Ω
In a series circuit, resistances add directly: R_eq = 7 Ω + 12 Ω = 19 Ω.
9. 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.
10. 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.
11. Two resistors of 16 Ω and 16 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
32 Ω
In a series circuit, resistances add directly: R_eq = 16 Ω + 16 Ω = 32 Ω.
12. Two resistors of 13 Ω and 15 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
28 Ω
In a series circuit, resistances add directly: R_eq = 13 Ω + 15 Ω = 28 Ω.

12 questions · Seed 56 · Age guidance, not curriculum certification