Activity 1.2 3 Electrical Circuits Answer Key

Activity 1.2.3 Electrical Circuits: A Comprehensive Guide with Answers

Understanding electrical circuits is fundamental to comprehending basic electronics. This comprehensive guide delves into Activity 1.2.3, a common assignment focusing on electrical circuits, providing detailed explanations, solved examples, and answers to solidify your understanding. We will cover key concepts like series circuits, parallel circuits, and combined series-parallel circuits, exploring their characteristics and how to solve problems related to voltage, current, and resistance.

What is Activity 1.2.3?

Activity 1.2.3 typically refers to a hands-on or theoretical exercise designed to test your knowledge of basic electrical circuit principles. It commonly involves analyzing different circuit configurations, calculating values like voltage (V), current (I), and resistance (R), and possibly troubleshooting simple circuit malfunctions. The specific problems within the activity will vary depending on the textbook or curriculum used, but the underlying principles remain consistent.

Essential Concepts: Ohm's Law and Circuit Types

Before diving into the answers, let's review crucial concepts:

1. Ohm's Law:

Ohm's Law is the bedrock of electrical circuit analysis. It states:

V = I * R

Where:

• V represents Voltage (measured in Volts) – the electrical potential difference driving the current.
• I represents Current (measured in Amperes) – the flow of electrical charge.
• R represents Resistance (measured in Ohms) – the opposition to current flow.

This law allows us to calculate any one of the three variables (V, I, or R) if we know the other two.

2. Series Circuits:

In a series circuit, components are connected end-to-end, forming a single path for current flow. Key characteristics include:

• Total Resistance (R_T): The total resistance is the sum of individual resistances: R_T = R₁ + R₂ + R₃ + ...
• Current (I): The current is the same throughout the entire circuit.
• Voltage (V): The total voltage is the sum of the voltage drops across each component: V_T = V₁ + V₂ + V₃ + ...

3. Parallel Circuits:

In a parallel circuit, components are connected across each other, providing multiple paths for current flow. Key characteristics include:

• Total Resistance (R_T): The reciprocal of the total resistance is the sum of the reciprocals of individual resistances: 1/R_T = 1/R₁ + 1/R₂ + 1/R₃ + ...
• Current (I): The total current is the sum of the currents flowing through each branch.
• Voltage (V): The voltage is the same across all components.

4. Combined Series-Parallel Circuits:

These circuits combine elements of both series and parallel configurations. Solving these requires breaking down the circuit into smaller, simpler series and parallel sections, calculating their equivalent resistances, and then combining them to find the overall circuit characteristics.

Solved Examples and Answers for Activity 1.2.3 (Hypothetical Scenarios)

Since the specific problems in Activity 1.2.3 are unknown, let's work through several hypothetical examples illustrating common circuit analysis problems. These examples cover series, parallel, and combined circuits, providing a comprehensive approach to solving such problems.

Example 1: Simple Series Circuit

A circuit consists of a 12V battery connected to three resistors: R₁ = 2Ω, R₂ = 4Ω, and R₃ = 6Ω.

a) Calculate the total resistance (R_T).

R_T = R₁ + R₂ + R₃ = 2Ω + 4Ω + 6Ω = 12Ω

b) Calculate the current (I) flowing through the circuit.

Using Ohm's Law: I = V/R_T = 12V / 12Ω = 1A

c) Calculate the voltage drop across each resistor.

• V₁ = I * R₁ = 1A * 2Ω = 2V
• V₂ = I * R₂ = 1A * 4Ω = 4V
• V₃ = I * R₃ = 1A * 6Ω = 6V

Note that V₁ + V₂ + V₃ = 12V, verifying Kirchhoff's Voltage Law.

Example 2: Simple Parallel Circuit

A circuit has a 12V battery connected to three resistors in parallel: R₁ = 6Ω, R₂ = 3Ω, and R₃ = 2Ω.

a) Calculate the total resistance (R_T).

1/R_T = 1/R₁ + 1/R₂ + 1/R₃ = 1/6Ω + 1/3Ω + 1/2Ω = 1Ω Therefore, R_T = 1Ω

b) Calculate the current (I) flowing through the circuit.

I = V/R_T = 12V / 1Ω = 12A

c) Calculate the current flowing through each resistor.

• I₁ = V/R₁ = 12V / 6Ω = 2A
• I₂ = V/R₂ = 12V / 3Ω = 4A
• I₃ = V/R₃ = 12V / 2Ω = 6A

Note that I₁ + I₂ + I₃ = 12A, verifying Kirchhoff's Current Law.

Example 3: Combined Series-Parallel Circuit

Consider a circuit with a 24V battery. R₁ = 4Ω is in series with a parallel combination of R₂ = 6Ω and R₃ = 3Ω.

a) Calculate the equivalent resistance of the parallel combination (R₂₃).

1/R₂₃ = 1/R₂ + 1/R₃ = 1/6Ω + 1/3Ω = 1/2Ω R₂₃ = 2Ω

b) Calculate the total resistance (R_T).

R_T = R₁ + R₂₃ = 4Ω + 2Ω = 6Ω

c) Calculate the total current (I) flowing from the battery.

I = V/R_T = 24V / 6Ω = 4A

d) Calculate the voltage drop across R₁ (V₁).

V₁ = I * R₁ = 4A * 4Ω = 16V

e) Calculate the voltage drop across the parallel combination (V₂₃).

V₂₃ = V - V₁ = 24V - 16V = 8V (This is also the voltage across R₂ and R₃ individually)

f) Calculate the current flowing through R₂ (I₂) and R₃ (I₃).

• I₂ = V₂₃ / R₂ = 8V / 6Ω = 4/3 A
• I₃ = V₂₃ / R₃ = 8V / 3Ω = 8/3 A

Note that I₂ + I₃ = 4A, which is equal to the total current entering the parallel branch.

Troubleshooting and Common Mistakes:

• Incorrect application of Ohm's Law: Double-check your units and ensure you're using the correct formula for series and parallel circuits.
• Misidentification of circuit type: Carefully analyze the circuit diagram to determine whether components are connected in series, parallel, or a combination.
• Calculation errors: Use a calculator and double-check your arithmetic.
• Incorrect interpretation of results: Make sure your answers make sense in the context of the circuit. For instance, the total resistance in a parallel circuit should always be less than the smallest individual resistance.

This comprehensive guide provides a solid foundation for understanding and solving problems related to Activity 1.2.3. Remember to practice with various circuit configurations to solidify your understanding and build confidence in solving complex electrical circuit problems. Remember to always consult your textbook and instructor for specific details regarding your assignment. This guide serves as a supplementary resource to aid your understanding.