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 solve them step by step, using Ohm’s Law and the rules for series circuits:

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🔧 Key Rules for Series Circuits:

1. Current (I) is the same everywhere in the circuit.
2. Total Voltage (Vₜ) = Sum of voltage drops across each resistor.
3. Total Resistance (Rₜ) = Sum of individual resistances:
$ R_T = R_1 + R_2 + R_3 + \dots $
4. Ohm’s Law: $ V = IR $ → $ I = \frac{V}{R} $, $ V = IR $

We'll analyze each problem.

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

Step-by-step:

- Total resistance:
$ R_T = 10\,\Omega + 20\,\Omega = 30\,\Omega $
- Total current:
$ I_T = \frac{V_T}{R_T} = \frac{90\,V}{30\,\Omega} = 3\,A $
- Current is same everywhere: $ I_1 = I_2 = 3\,A $
- Voltage drop across R₁:
$ V_1 = I \cdot R_1 = 3\,A \times 10\,\Omega = 30\,V $
- Voltage drop across R₂:
$ V_2 = 3\,A \times 20\,\Omega = 60\,V $

✔ Correct!
Answer:
- $ R_T = 30\,\Omega $, $ I_T = 3\,A $, $ V_1 = 30\,V $, $ V_2 = 60\,V $

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

Step-by-step:

- $ R_T = 6 + 14 + 10 = 30\,\Omega $
- $ I_T = \frac{60\,V}{30\,\Omega} = 2\,A $ ← Wait! But student wrote 3 amps ✘

Wait — let's check:
- Student says: $ I_T = 3\,A $? That would mean $ R_T = \frac{60}{3} = 20\,\Omega $, but actual total resistance is 30 Ω, so current should be 2 A

✘ Error here!

Let’s correct it:

- $ I_T = \frac{60}{30} = 2\,A $
- So $ I_1 = I_2 = I_3 = 2\,A $
- $ V_1 = 2\,A \times 6\,\Omega = 12\,V $
- $ V_2 = 2\,A \times 14\,\Omega = 28\,V $
- $ V_3 = 2\,A \times 10\,\Omega = 20\,V $

But student has:
- $ I_T = 3\,A $ → ✘
- $ V_1 = 18\,V $ → only possible if $ I = 3\,A $, but that’s wrong

✔ Correct Answer:
- $ R_T = 30\,\Omega $
- $ I_T = 2\,A $
- $ V_1 = 12\,V $, $ V_2 = 28\,V $, $ V_3 = 20\,V $

✘ Student made a mistake here.

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## ✔ Problem 3:
- Battery: 75 V
- R₁ = 10 Ω
- Ammeter shows 5 A → so $ I_T = 5\,A $
- Voltmeter across R₂ shows 25 V → $ V_2 = 25\,V $

Find: $ V_1 $, $ I_2 $, $ R_2 $

Step-by-step:

- Since it's series: $ I_T = I_1 = I_2 = 5\,A $
- $ V_1 = I_1 \cdot R_1 = 5\,A \times 10\,\Omega = 50\,V $
- Total voltage: $ V_T = V_1 + V_2 = 50\,V + 25\,V = 75\,V $ → matches battery
- $ R_2 = \frac{V_2}{I_2} = \frac{25\,V}{5\,A} = 5\,\Omega $

But student wrote:
- $ V_1 = 50\,V $ ✔
- $ I_2 = 5\,amps $ ✔
- $ R_2 = 10\,\Omega $ ✘ → Should be 5 Ω

✔ Correction: $ R_2 = 5\,\Omega $

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## ✔ Problem 4:
- R₁ = 5 Ω, R₂ = 15 Ω
- Current shown: 5 A → $ I_T = 5\,A $
- Find: $ V_1 $, $ V_2 $, $ V_T $

Step-by-step:

- $ V_1 = I \cdot R_1 = 5\,A \times 5\,\Omega = 25\,V $
- $ V_2 = 5\,A \times 15\,\Omega = 75\,V $
- $ V_T = 25\,V + 75\,V = 100\,V $

✔ Student answers:
- $ V_1 = 25\,V $ ✔
- $ V_2 = 75\,V $ ✔
- $ V_T = 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:

- $ R_T = 5 + 3 + 2 = 10\,\Omega $
- $ I_T = \frac{20\,V}{10\,\Omega} = 2\,A $
- $ V_1 = 2\,A \times 5\,\Omega = 10\,V $
- $ V_2 = 2\,A \times 3\,\Omega = 6\,V $
- $ V_3 = 2\,A \times 2\,\Omega = 4\,V $

Student has:
- $ R_T = 10\,\Omega $ ✔
- $ I_T = 2\,A $ ✔
- $ V_1 = 10\,V $ ✔
- $ V_2 = 6\,V $ ✔
- $ V_3 = 4\,V $ ✔

✔️ All correct!

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## ✔ Problem 6:
- Battery: 40 V
- R₃ = 10 Ω, with 20 V across it
- Voltmeter across R₂ shows 10 V
- Given: $ I_3 = 2\,A $

Step-by-step:

- $ I_3 = 2\,A $ → since series, $ I_1 = I_2 = I_3 = 2\,A $
- Voltage across R₃: $ V_3 = 20\,V $ (given)
- Voltage across R₂: $ V_2 = 10\,V $ (given)
- Total voltage: $ V_T = V_1 + V_2 + V_3 = ? $
- But battery is 40 V → so $ V_1 = 40 - 20 - 10 = 10\,V $

Now find resistances:
- $ R_3 = \frac{V_3}{I_3} = \frac{20\,V}{2\,A} = 10\,\Omega $ → given ✔
- $ R_2 = \frac{V_2}{I_2} = \frac{10\,V}{2\,A} = 5\,\Omega $
- $ R_1 = \frac{V_1}{I_1} = \frac{10\,V}{2\,A} = 5\,\Omega $

Student has:
- $ I_3 = 2\,A $ ✔
- $ I_1 = 2\,A $ ✔
- $ V_1 = 10\,V $ ✔
- $ R_1 = 5\,\Omega $ ✔
- $ R_2 = 5\,\Omega $ ✔

✔️ All correct!

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## 📌 Summary of Corrections:

| Problem | Error? | Correction |
|--------|--------|-----------|
| 1 | ✔ | Correct |
| 2 | ✘ | $ I_T = 2\,A $, not 3 A; $ V_1 = 12\,V $, $ V_2 = 28\,V $, $ V_3 = 20\,V $ |
| 3 | ✘ | $ R_2 = 5\,\Omega $, not 10 Ω |
| 4 | ✔ | Correct |
| 5 | ✔ | Correct |
| 6 | ✔ | Correct |

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## ✔ Final Answers (Corrected):

1)

- $ R_T = 30\,\Omega $
- $ I_T = 3\,A $
- $ V_1 = 30\,V $, $ V_2 = 60\,V $

2) CORRECTED

- $ R_T = 30\,\Omega $
- $ I_T = 2\,A $
- $ V_1 = 12\,V $, $ V_2 = 28\,V $, $ V_3 = 20\,V $

3) CORRECTED

- $ V_1 = 50\,V $
- $ I_2 = 5\,A $
- $ R_2 = 5\,\Omega $

4)

- $ V_1 = 25\,V $
- $ V_2 = 75\,V $
- $ V_T = 100\,V $

5)

- $ R_T = 10\,\Omega $
- $ I_T = 2\,A $
- $ V_1 = 10\,V $, $ V_2 = 6\,V $, $ V_3 = 4\,V $

6)

- $ I_3 = 2\,A $
- $ I_1 = 2\,A $
- $ V_1 = 10\,V $
- $ R_1 = 5\,\Omega $
- $ R_2 = 5\,\Omega $

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