Revisão Resistores em Série e Paralelo (Exercícios resolvidos e teoria)
Table of Contents
Introduction
This tutorial provides a comprehensive guide on understanding and calculating electrical circuits with resistors in series and parallel. It covers theoretical concepts and practical exercises to help solidify your knowledge of how current flows, how to calculate equivalent resistance, and how to determine the voltage across each resistor.
Step 1: Understanding Resistors in Series
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Definition: In a series circuit, resistors are connected end-to-end, meaning the same current flows through each resistor.
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Key Formula: The total resistance ( R_{total} ) in a series circuit is the sum of the individual resistances: [ R_{total} = R_1 + R_2 + R_3 + ... ]
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Practical Tip: Ensure to check the specifications of each resistor to avoid exceeding the power rating.
Step 2: Understanding Resistors in Parallel
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Definition: In a parallel circuit, resistors are connected across the same two points, providing multiple paths for the current to flow.
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Key Formula: The total resistance ( R_{total} ) for resistors in parallel is given by: [ \frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + ... ]
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Practical Tip: Each resistor in parallel experiences the same voltage across its terminals.
Step 3: Calculating Resistance for a Lamp Connection
- Problem: A lamp designed for 60 W and 120 V needs to be connected to a 220 V supply.
- Calculation:
- First, calculate the lamp's resistance ( R_{lamp} ): [ R_{lamp} = \frac{V^2}{P} = \frac{120^2}{60} = 240 , \Omega ]
- Determine the required series resistor ( R_{series} ) to reduce voltage: [ V_{total} = V_{lamp} + V_{series} ] [ R_{series} = \frac{(220 - 120)}{I} ] where ( I ) is the current through the lamp, calculated from ( P = V \times I ).
Step 4: Calculating Equivalent Resistance and Current
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Given: Three resistors ( R_1 = 60 , \Omega ), ( R_2 = 30 , \Omega ), and ( R_3 = 20 , \Omega ) in parallel with a 120 V supply.
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Calculation of Equivalent Resistance: [ \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} = \frac{1}{60} + \frac{1}{30} + \frac{1}{20} ]
- Solve for ( R_{eq} ).
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Calculate Total Current: [ I_{total} = \frac{V}{R_{eq}} ]
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Voltage across Each Resistor: Since they are in parallel, ( V = 120 , V ) for all.
Step 5: Finding Current in Each Resistor
- Formulas:
- For each resistor in parallel: [ I_n = \frac{V}{R_n} ]
- Calculate:
- For ( R_1 ): [ I_1 = \frac{120}{60} = 2 , A ]
- For ( R_2 ): [ I_2 = \frac{120}{30} = 4 , A ]
- For ( R_3 ): [ I_3 = \frac{120}{20} = 6 , A ]
Conclusion
In this tutorial, we covered the fundamentals of resistors in series and parallel circuits, calculations for equivalent resistance, and how to determine the current through each resistor. Understanding these concepts is crucial for working with electrical circuits. For further practice, consider solving additional problems involving different resistor values and configurations.