Worksheet - Series Circuit Problems - Worksheet- Series Circuit ... - Free Printable

Let's go through each of the six series circuit problems on this worksheet and verify or correct the answers based on Ohm’s Law and series circuit rules.

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🔧 Series Circuit Rules Recap:

1. Current (I) is the same everywhere in a series circuit.
2. Total Resistance (Rₜ) = R₁ + R₂ + R₃ + ...
3. Total Voltage (Vₜ) = V₁ + V₂ + V₃ + ...
4. Ohm’s Law:
- V = I × R
- I = V / R
- R = V / I

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We'll analyze each problem one by one.

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## ✔ Problem 1:
- Battery voltage: 90 V
- R₁ = 10 Ω, R₂ = 20 Ω
- All in series

Step-by-step:

- Total resistance:
Rₜ = R₁ + R₂ = 10 + 20 = 30 Ω

- Total current:
Iₜ = Vₜ / Rₜ = 90 V / 30 Ω = 3 A

- Current through each resistor:
I₁ = I₂ = Iₜ = 3 A

- Voltage across each:
- V₁ = I × R₁ = 3 × 10 = 30 V
- V₂ = I × R₂ = 3 × 20 = 60 V

✔ All values are correct.

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## ✔ Problem 2:
- Battery: 60 V
- R₁ = 6 Ω, R₂ = 14 Ω, R₃ = 10 Ω

Step-by-step:

- Rₜ = 6 + 14 + 10 = 30 Ω
- Iₜ = 60 V / 30 Ω = 2 A ← Wait! The student wrote 3 amps, which is wrong.

But the student says:
> Rₜ = 30Ω, Iₜ = 3 amps → ✘ Incorrect!

Let’s fix:

- Iₜ = 60 / 30 = 2 A

Then:
- V₁ = I × R₁ = 2 × 6 = 12 V
- V₂ = 2 × 14 = 28 V
- V₃ = 2 × 10 = 20 V

But the student wrote:
> V₁ = 18 V, V₂ = 42 V, V₃ = 30 V → ✘ All wrong.

So the student made an error here.

✔ Corrected Answers:
- Rₜ = 30 Ω
- Iₜ = 2 A
- I₁ = I₂ = I₃ = 2 A
- V₁ = 12 V, V₂ = 28 V, V₃ = 20 V

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## ✔ Problem 3:
- Battery: 75 V
- R₁ = 10 Ω
- Ammeter reads 5 A
- Voltmeter across R₂ reads 25 V

Given:

- Current I = 5 A (from ammeter)
- Voltage across R₂ = 25 V

Find:

- V₁ = ?
- I₂ = ?
- R₂ = ?

Since it's a series circuit, current is the same everywhere → I₂ = 5 A

Voltage drop across R₁:
- V₁ = V_total − V₂ = 75 − 25 = 50 V

Now use Ohm’s Law to find R₂:
- R₂ = V₂ / I = 25 V / 5 A = 5 Ω

Wait — but the student wrote R₂ = 10 Ω → ✘ Incorrect

✔ Corrected Answers:
- V₁ = 50 V ✔
- I₂ = 5 A ✔
- R₂ = 5 Ω ✘ (student said 10 Ω)

So the student likely miscalculated R₂.

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## ✔ Problem 4:
- R₁ = 5 Ω, R₂ = 15 Ω
- Ammeter shows 5 A
- Find: V₁, V₂, Vₜ

Step-by-step:

- I = 5 A (same everywhere)
- V₁ = I × R₁ = 5 × 5 = 25 V
- V₂ = 5 × 15 = 75 V
- Vₜ = V₁ + V₂ = 25 + 75 = 100 V

✔ Student's answers:
- V₁ = 25 V ✔
- V₂ = 75 V ✔
- Vₜ = 100 V ✔

All correct.

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## ✔ Problem 5:
- Battery: 20 V
- R₁ = 5 Ω, R₂ = 3 Ω, R₃ = 2 Ω

Step-by-step:

- Rₜ = 5 + 3 + 2 = 10 Ω
- Iₜ = V / Rₜ = 20 / 10 = 2 A

Now:
- V₁ = 2 × 5 = 10 V
- V₂ = 2 × 3 = 6 V
- V₃ = 2 × 2 = 4 V

Student wrote:
- Rₜ = 10 Ω ✔
- Iₜ = 2 A ✔
- V₁ = 10 V ✔
- V₂ = 6 V ✔
- V₃ = 4 V ✔

✔ All correct.

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## ✔ Problem 6:
- Battery: 40 V
- R₃ = 10 Ω
- Voltmeter across R₃ shows 20 V
- Voltmeter across R₂ shows 10 V
- Find: I₃, I₁, V₁, R₁, R₂

Step-by-step:

- Since it's a series circuit, current is same everywhere → I₁ = I₂ = I₃
- Voltage across R₃ = 20 V, R₃ = 10 Ω
- So I₃ = V₃ / R₃ = 20 / 10 = 2 A
→ Therefore, I₁ = I₂ = I₃ = 2 A

- Voltage across R₂ = 10 V → V₂ = 10 V
- So R₂ = V₂ / I = 10 / 2 = 5 Ω

- Total voltage: Vₜ = V₁ + V₂ + V₃ = 40 V
- We know V₂ = 10 V, V₃ = 20 V → V₁ = 40 − 10 − 20 = 10 V

- Now R₁ = V₁ / I = 10 / 2 = 5 Ω

Student wrote:
- I₃ = 2 amps ✔
- I₁ = 2 amps ✔
- V₁ = 10 V ✔
- R₁ = 5 Ω ✔
- R₂ = 5 Ω ✔

✔ All correct.

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📝 Summary of Corrections:

| Problem | Error? | Correction |
|--------|--------|-----------|
| 1 | ✔ Correct | All good |
| 2 | ✘ Wrong | Iₜ = 2 A, not 3 A; V₁=12V, V₂=28V, V₃=20V |
| 3 | ✘ Wrong | R₂ = 5 Ω, not 10 Ω |
| 4 | ✔ Correct | All good |
| 5 | ✔ Correct | All good |
| 6 | ✔ Correct | All good |

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✔ Final Answer Summary:

#### Problem 1:
- Rₜ = 30 Ω, I = 3 A, V₁ = 30 V, V₂ = 60 V → ✔️

#### Problem 2:
- Rₜ = 30 Ω, I = 2 A, V₁ = 12 V, V₂ = 28 V, V₃ = 20 V → ✔ (corrected)

#### Problem 3:
- V₁ = 50 V, I₂ = 5 A, R₂ = 5 Ω → ✔ (corrected)

#### Problem 4:
- V₁ = 25 V, V₂ = 75 V, Vₜ = 100 V → ✔️

#### Problem 5:
- Rₜ = 10 Ω, I = 2 A, V₁ = 10 V, V₂ = 6 V, V₃ = 4 V → ✔️

#### Problem 6:
- I₃ = 2 A, I₁ = 2 A, V₁ = 10 V, R₁ = 5 Ω, R₂ = 5 Ω → ✔️

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