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 21 Ω and 25 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 21 Ω, R₂ = 25 Ω · R_eq = R₁ + R₂ = ?
2. Two resistors of 3 Ω and 23 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 3 Ω, R₂ = 23 Ω · R_eq = R₁ + R₂ = ?
3. 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
4. Two resistors of 18 Ω and 16 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 18 Ω, R₂ = 16 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 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
7. Two resistors of 2 Ω and 2 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 2 Ω, R₂ = 2 Ω · R_eq = R₁ + R₂ = ?
8. Two resistors of 36 Ω and 180 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 36 Ω ∥ 180 Ω · 1/R_eq = 1/36 + 1/180
9. Two resistors of 5 Ω and 17 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 5 Ω, R₂ = 17 Ω · R_eq = R₁ + R₂ = ?
10. Two resistors of 36 Ω and 72 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 36 Ω ∥ 72 Ω · 1/R_eq = 1/36 + 1/72
11. 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
12. Two resistors of 22 Ω and 24 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 22 Ω, R₂ = 24 Ω · R_eq = R₁ + R₂ = ?

12 questions · Seed 48 · 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 21 Ω and 25 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
46 Ω
In a series circuit, resistances add directly: R_eq = 21 Ω + 25 Ω = 46 Ω.
2. Two resistors of 3 Ω and 23 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
26 Ω
In a series circuit, resistances add directly: R_eq = 3 Ω + 23 Ω = 26 Ω.
3. 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.
4. Two resistors of 18 Ω and 16 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
34 Ω
In a series circuit, resistances add directly: R_eq = 18 Ω + 16 Ω = 34 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 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.
7. Two resistors of 2 Ω and 2 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
4 Ω
In a series circuit, resistances add directly: R_eq = 2 Ω + 2 Ω = 4 Ω.
8. Two resistors of 36 Ω and 180 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
30 Ω
For two parallel resistors, R_eq = (36 × 180) ÷ (36 + 180) = 6480 ÷ 216 = 30 Ω.
9. Two resistors of 5 Ω and 17 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
22 Ω
In a series circuit, resistances add directly: R_eq = 5 Ω + 17 Ω = 22 Ω.
10. Two resistors of 36 Ω and 72 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
24 Ω
For two parallel resistors, R_eq = (36 × 72) ÷ (36 + 72) = 2592 ÷ 108 = 24 Ω.
11. 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.
12. Two resistors of 22 Ω and 24 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
46 Ω
In a series circuit, resistances add directly: R_eq = 22 Ω + 24 Ω = 46 Ω.

12 questions · Seed 48 · 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 21 Ω and 25 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 21 Ω, R₂ = 25 Ω · R_eq = R₁ + R₂ = ?
2. Two resistors of 3 Ω and 23 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 3 Ω, R₂ = 23 Ω · R_eq = R₁ + R₂ = ?
3. 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
4. Two resistors of 18 Ω and 16 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 18 Ω, R₂ = 16 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 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
7. Two resistors of 2 Ω and 2 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 2 Ω, R₂ = 2 Ω · R_eq = R₁ + R₂ = ?
8. Two resistors of 36 Ω and 180 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 36 Ω ∥ 180 Ω · 1/R_eq = 1/36 + 1/180
9. Two resistors of 5 Ω and 17 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 5 Ω, R₂ = 17 Ω · R_eq = R₁ + R₂ = ?
10. Two resistors of 36 Ω and 72 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 36 Ω ∥ 72 Ω · 1/R_eq = 1/36 + 1/72
11. 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
12. Two resistors of 22 Ω and 24 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 22 Ω, R₂ = 24 Ω · R_eq = R₁ + R₂ = ?

12 questions · Seed 48 · 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 21 Ω and 25 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
46 Ω
In a series circuit, resistances add directly: R_eq = 21 Ω + 25 Ω = 46 Ω.
2. Two resistors of 3 Ω and 23 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
26 Ω
In a series circuit, resistances add directly: R_eq = 3 Ω + 23 Ω = 26 Ω.
3. 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.
4. Two resistors of 18 Ω and 16 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
34 Ω
In a series circuit, resistances add directly: R_eq = 18 Ω + 16 Ω = 34 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 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.
7. Two resistors of 2 Ω and 2 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
4 Ω
In a series circuit, resistances add directly: R_eq = 2 Ω + 2 Ω = 4 Ω.
8. Two resistors of 36 Ω and 180 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
30 Ω
For two parallel resistors, R_eq = (36 × 180) ÷ (36 + 180) = 6480 ÷ 216 = 30 Ω.
9. Two resistors of 5 Ω and 17 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
22 Ω
In a series circuit, resistances add directly: R_eq = 5 Ω + 17 Ω = 22 Ω.
10. Two resistors of 36 Ω and 72 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
24 Ω
For two parallel resistors, R_eq = (36 × 72) ÷ (36 + 72) = 2592 ÷ 108 = 24 Ω.
11. 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.
12. Two resistors of 22 Ω and 24 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
46 Ω
In a series circuit, resistances add directly: R_eq = 22 Ω + 24 Ω = 46 Ω.

12 questions · Seed 48 · Age guidance, not curriculum certification