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 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
2. Two resistors of 12 Ω and 16 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 12 Ω, R₂ = 16 Ω · R_eq = R₁ + R₂ = ?
3. Two resistors of 3 Ω and 20 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 3 Ω, R₂ = 20 Ω · R_eq = R₁ + R₂ = ?
4. Two resistors of 25 Ω and 22 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 25 Ω, R₂ = 22 Ω · R_eq = R₁ + R₂ = ?
5. Two resistors of 4 Ω and 22 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 4 Ω, R₂ = 22 Ω · R_eq = R₁ + R₂ = ?
6. Two resistors of 22 Ω and 23 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 22 Ω, R₂ = 23 Ω · R_eq = R₁ + R₂ = ?
7. Two resistors of 30 Ω and 150 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 30 Ω ∥ 150 Ω · 1/R_eq = 1/30 + 1/150
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 32 Ω and 96 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 32 Ω ∥ 96 Ω · 1/R_eq = 1/32 + 1/96
10. Two resistors of 2 Ω and 20 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 2 Ω, R₂ = 20 Ω · R_eq = R₁ + R₂ = ?
11. Two resistors of 19 Ω and 2 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 19 Ω, R₂ = 2 Ω · R_eq = R₁ + R₂ = ?
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 53 · 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 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.
2. Two resistors of 12 Ω and 16 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
28 Ω
In a series circuit, resistances add directly: R_eq = 12 Ω + 16 Ω = 28 Ω.
3. Two resistors of 3 Ω and 20 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
23 Ω
In a series circuit, resistances add directly: R_eq = 3 Ω + 20 Ω = 23 Ω.
4. Two resistors of 25 Ω and 22 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
47 Ω
In a series circuit, resistances add directly: R_eq = 25 Ω + 22 Ω = 47 Ω.
5. Two resistors of 4 Ω and 22 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
26 Ω
In a series circuit, resistances add directly: R_eq = 4 Ω + 22 Ω = 26 Ω.
6. Two resistors of 22 Ω and 23 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
45 Ω
In a series circuit, resistances add directly: R_eq = 22 Ω + 23 Ω = 45 Ω.
7. Two resistors of 30 Ω and 150 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
25 Ω
For two parallel resistors, R_eq = (30 × 150) ÷ (30 + 150) = 4500 ÷ 180 = 25 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 32 Ω and 96 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
24 Ω
For two parallel resistors, R_eq = (32 × 96) ÷ (32 + 96) = 3072 ÷ 128 = 24 Ω.
10. Two resistors of 2 Ω and 20 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
22 Ω
In a series circuit, resistances add directly: R_eq = 2 Ω + 20 Ω = 22 Ω.
11. Two resistors of 19 Ω and 2 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
21 Ω
In a series circuit, resistances add directly: R_eq = 19 Ω + 2 Ω = 21 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 53 · 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 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
2. Two resistors of 12 Ω and 16 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 12 Ω, R₂ = 16 Ω · R_eq = R₁ + R₂ = ?
3. Two resistors of 3 Ω and 20 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 3 Ω, R₂ = 20 Ω · R_eq = R₁ + R₂ = ?
4. Two resistors of 25 Ω and 22 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 25 Ω, R₂ = 22 Ω · R_eq = R₁ + R₂ = ?
5. Two resistors of 4 Ω and 22 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 4 Ω, R₂ = 22 Ω · R_eq = R₁ + R₂ = ?
6. Two resistors of 22 Ω and 23 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 22 Ω, R₂ = 23 Ω · R_eq = R₁ + R₂ = ?
7. Two resistors of 30 Ω and 150 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 30 Ω ∥ 150 Ω · 1/R_eq = 1/30 + 1/150
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 32 Ω and 96 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
Parallel: 32 Ω ∥ 96 Ω · 1/R_eq = 1/32 + 1/96
10. Two resistors of 2 Ω and 20 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 2 Ω, R₂ = 20 Ω · R_eq = R₁ + R₂ = ?
11. Two resistors of 19 Ω and 2 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
Series: R₁ = 19 Ω, R₂ = 2 Ω · R_eq = R₁ + R₂ = ?
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 53 · 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 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.
2. Two resistors of 12 Ω and 16 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
28 Ω
In a series circuit, resistances add directly: R_eq = 12 Ω + 16 Ω = 28 Ω.
3. Two resistors of 3 Ω and 20 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
23 Ω
In a series circuit, resistances add directly: R_eq = 3 Ω + 20 Ω = 23 Ω.
4. Two resistors of 25 Ω and 22 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
47 Ω
In a series circuit, resistances add directly: R_eq = 25 Ω + 22 Ω = 47 Ω.
5. Two resistors of 4 Ω and 22 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
26 Ω
In a series circuit, resistances add directly: R_eq = 4 Ω + 22 Ω = 26 Ω.
6. Two resistors of 22 Ω and 23 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
45 Ω
In a series circuit, resistances add directly: R_eq = 22 Ω + 23 Ω = 45 Ω.
7. Two resistors of 30 Ω and 150 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
25 Ω
For two parallel resistors, R_eq = (30 × 150) ÷ (30 + 150) = 4500 ÷ 180 = 25 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 32 Ω and 96 Ω are connected in parallel. Using R_eq = (R₁ × R₂) ÷ (R₁ + R₂), calculate their equivalent resistance.
24 Ω
For two parallel resistors, R_eq = (32 × 96) ÷ (32 + 96) = 3072 ÷ 128 = 24 Ω.
10. Two resistors of 2 Ω and 20 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
22 Ω
In a series circuit, resistances add directly: R_eq = 2 Ω + 20 Ω = 22 Ω.
11. Two resistors of 19 Ω and 2 Ω are connected in series across a circuit. Calculate their combined equivalent resistance.
21 Ω
In a series circuit, resistances add directly: R_eq = 19 Ω + 2 Ω = 21 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 53 · Age guidance, not curriculum certification