SOLUTION: 1 series circuits module - Studypool - Free Printable

Let's solve each problem on the Series Circuit Worksheet #2 using Ohm’s Law and principles of series circuits.

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🔧 Key Concepts for Series Circuits:

1. Total Resistance (Rₜ):
$$
R_T = R_1 + R_2 + R_3 + \dots
$$

2. Current (I): Same through all components in a series circuit.
$$
I_T = \frac{E}{R_T}
$$

3. Voltage (E):
$$
E = I_T \times R_T
$$

4. Ohm’s Law:
$$
V = I \times R, \quad I = \frac{V}{R}, \quad R = \frac{V}{I}
$$

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Now let's go through each question one by one.

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Problem 1

Given:
- R₁ = 1 Ω
- R₂ = 1 Ω
- R₃ = 1 Ω
- Iₜ = 8 A
- Find: E (voltage)

#### Step 1: Total Resistance
$$
R_T = R_1 + R_2 + R_3 = 1 + 1 + 1 = 3\ \Omega
$$

#### Step 2: Use Ohm’s Law to find Voltage
$$
E = I_T \times R_T = 8\ \text{A} \times 3\ \Omega = 24\ \text{volts}
$$

✔ Answer: E = 24 volts

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Problem 2

Given:
- E = 24 volts
- R₁ = 2 Ω
- R₂ = 2 Ω
- R₃ = 2 Ω
- Find: Iₜ (current)

#### Step 1: Total Resistance
$$
R_T = 2 + 2 + 2 = 6\ \Omega
$$

#### Step 2: Current
$$
I_T = \frac{E}{R_T} = \frac{24}{6} = 4\ \text{amperes}
$$

✔ Answer: Iₜ = 4 amperes

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Problem 3

Given:
- E = 24 volts
- Iₜ = 4 amperes
- R₁ = 2 Ω
- R₂ = 1 Ω
- R₃ = ?
- Find: R₃

#### Step 1: Total Resistance
Use Ohm’s Law:
$$
R_T = \frac{E}{I_T} = \frac{24}{4} = 6\ \Omega
$$

#### Step 2: Solve for R₃
$$
R_T = R_1 + R_2 + R_3 \\
6 = 2 + 1 + R_3 \\
R_3 = 6 - 3 = 3\ \Omega
$$

✔ Answer: R₃ = 3 ohms

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Problem 4

Given:
- E = 12 volts
- Iₜ = 2 amperes
- R₁ = 1 Ω
- R₂ = 2 Ω
- R₃ = 1 Ω
- R₄ = ?
- Find: R₄

#### Step 1: Total Resistance
$$
R_T = \frac{E}{I_T} = \frac{12}{2} = 6\ \Omega
$$

#### Step 2: Add known resistances
$$
R_1 + R_2 + R_3 = 1 + 2 + 1 = 4\ \Omega
$$

$$
R_T = R_1 + R_2 + R_3 + R_4 \\
6 = 4 + R_4 \\
R_4 = 2\ \Omega
$$

✔ Answer: R₄ = 2 ohms

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Problem 5

Given:
- E = 24 volts
- Iₜ = 2 amperes
- R₁ = 2 Ω
- R₂ = 4 Ω
- R₃ = 1 Ω
- R₄ = ?
- Find: R₄

#### Step 1: Total Resistance
$$
R_T = \frac{E}{I_T} = \frac{24}{2} = 12\ \Omega
$$

#### Step 2: Sum of known resistors
$$
R_1 + R_2 + R_3 = 2 + 4 + 1 = 7\ \Omega
$$

$$
R_T = R_1 + R_2 + R_3 + R_4 \\
12 = 7 + R_4 \\
R_4 = 5\ \Omega
$$

✔ Answer: R₄ = 5 ohms

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Problem 6

Given:
- Iₜ = 3 amperes
- R₁ = 2 Ω
- R₂ = 1 Ω
- R₃ = 2 Ω
- R₄ = 1 Ω
- Find: E (voltage)

#### Step 1: Total Resistance
$$
R_T = 2 + 1 + 2 + 1 = 6\ \Omega
$$

#### Step 2: Use Ohm’s Law
$$
E = I_T \times R_T = 3 \times 6 = 18\ \text{volts}
$$

✔ Answer: E = 18 volts

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✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1 | E = 24 volts |
| 2 | Iₜ = 4 amperes |
| 3 | R₃ = 3 ohms |
| 4 | R₄ = 2 ohms |
| 5 | R₄ = 5 ohms |
| 6 | E = 18 volts |

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📝 Explanation Recap:

All these are series circuits, so:
- Current is the same everywhere.
- Resistances add directly.
- Voltage divides across resistors based on resistance values.

We used Ohm’s Law (V = IR) and total resistance rules to solve each unknown.

Let me know if you'd like this turned into a printable answer key or need help with parallel circuits too!