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(ii) the magnitude of power dissipated through resistance Ri and (iil) the magnitude of power dissipated through resistance Ra.

(ii) the magnitude of power dissipated through resistance Ri and (iil) the magnitude of power dissipated through resistance Ra.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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### Problem Statement: **Given:** - \( R_1 = 10 \, \Omega \) - \( R_2 = 15 \, \Omega \) - \( R_3 = 22 \, \Omega \) - \( R_4 = 10 \, \Omega \) **Objective:** Find (i) the equivalent resistance of the circuit, (ii) the magnitude of power dissipated through resistance \( R_3 \), and (iii) the magnitude of power dissipated through resistance \( R_4 \). ### Diagram Explanation: The circuit diagram consists of four resistors \( R_1, R_2, R_3, \) and \( R_4 \) connected to a 12V battery. - \( R_1 \) and \( R_2 \) are connected in parallel. - \( R_3 \) is connected in series with the parallel combination of \( R_1 \) and \( R_2 \). - \( R_4 \) is also connected in series with the remaining combination. ### Analyses Required: 1. **Equivalent Resistance Calculation:** - Calculate the equivalent resistance for \( R_1 \) and \( R_2 \) in parallel. - Add the equivalent resistance of \( R_1 \) and \( R_2 \) with \( R_3 \) and \( R_4 \) in series. 2. **Power Calculation:** - Use the formula \( P = I^2 R \) or \( P = \frac{V^2}{R} \) to calculate power dissipation across \( R_3 \) and \( R_4 \), where \( V \) is the voltage across the resistor and \( I \) is the current through the resistor. This setup allows learners to practice using series and parallel circuit rules to solve for resistance and power in electrical circuits.
Transcribed Image Text:### Problem Statement: **Given:** - \( R_1 = 10 \, \Omega \) - \( R_2 = 15 \, \Omega \) - \( R_3 = 22 \, \Omega \) - \( R_4 = 10 \, \Omega \) **Objective:** Find (i) the equivalent resistance of the circuit, (ii) the magnitude of power dissipated through resistance \( R_3 \), and (iii) the magnitude of power dissipated through resistance \( R_4 \). ### Diagram Explanation: The circuit diagram consists of four resistors \( R_1, R_2, R_3, \) and \( R_4 \) connected to a 12V battery. - \( R_1 \) and \( R_2 \) are connected in parallel. - \( R_3 \) is connected in series with the parallel combination of \( R_1 \) and \( R_2 \). - \( R_4 \) is also connected in series with the remaining combination. ### Analyses Required: 1. **Equivalent Resistance Calculation:** - Calculate the equivalent resistance for \( R_1 \) and \( R_2 \) in parallel. - Add the equivalent resistance of \( R_1 \) and \( R_2 \) with \( R_3 \) and \( R_4 \) in series. 2. **Power Calculation:** - Use the formula \( P = I^2 R \) or \( P = \frac{V^2}{R} \) to calculate power dissipation across \( R_3 \) and \( R_4 \), where \( V \) is the voltage across the resistor and \( I \) is the current through the resistor. This setup allows learners to practice using series and parallel circuit rules to solve for resistance and power in electrical circuits.
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