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he circuit element below, determine the current I in the circuit and ree resistors: (Provide your calculations and reasoning for your ar Vs = 15 V R1 = 220 2 R2 = 470 2 R3 = 1.0 k2

he circuit element below, determine the current I in the circuit and ree resistors: (Provide your calculations and reasoning for your ar Vs = 15 V R1 = 220 2 R2 = 470 2 R3 = 1.0 k2

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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## Circuit Analysis Problem ### Problem Statement For the circuit element below, determine the current \( I \) in the circuit and the voltage across each of the three resistors. Provide your calculations and reasoning for your answer. ### Given Values - \( V_s = 15 \, \text{V} \) - \( R_1 = 220 \, \Omega \) - \( R_2 = 470 \, \Omega \) - \( R_3 = 1.0 \, \text{k}\Omega \) ### Circuit Description The circuit is a simple series circuit consisting of: - A voltage source \( V_s \) - Three resistors \( R_1 \), \( R_2 \), and \( R_3 \) connected in series ### Diagram Explanation The diagram shows the series circuit with: - A voltage source represented as \( V_s \) with positive and negative terminals. - Current \( I \) flowing clockwise from the positive terminal of the voltage source through each resistor \( R_1 \), \( R_2 \), and \( R_3 \), then back to the negative terminal. ### Solution 1. **Calculate Total Resistance**: The total resistance \( R_t \) for resistors in series is the sum of their resistances: \[ R_t = R_1 + R_2 + R_3 = 220 \, \Omega + 470 \, \Omega + 1000 \, \Omega = 1690 \, \Omega \] 2. **Determine the Current \( I \)**: Using Ohm's Law, \( V = IR \), the current \( I \) in the circuit is given by: \[ I = \frac{V_s}{R_t} = \frac{15 \, \text{V}}{1690 \, \Omega} \approx 0.00888 \, \text{A} \, \text{(or 8.88 mA)} \] 3. **Calculate the Voltage Across Each Resistor**: - **Voltage across \( R_1 \)**: \[ V_1 = I \times R_1 = 0.00888 \, \text{A} \times 220 \, \Omega = 1.9536 \, \text{V} \]
Transcribed Image Text:## Circuit Analysis Problem ### Problem Statement For the circuit element below, determine the current \( I \) in the circuit and the voltage across each of the three resistors. Provide your calculations and reasoning for your answer. ### Given Values - \( V_s = 15 \, \text{V} \) - \( R_1 = 220 \, \Omega \) - \( R_2 = 470 \, \Omega \) - \( R_3 = 1.0 \, \text{k}\Omega \) ### Circuit Description The circuit is a simple series circuit consisting of: - A voltage source \( V_s \) - Three resistors \( R_1 \), \( R_2 \), and \( R_3 \) connected in series ### Diagram Explanation The diagram shows the series circuit with: - A voltage source represented as \( V_s \) with positive and negative terminals. - Current \( I \) flowing clockwise from the positive terminal of the voltage source through each resistor \( R_1 \), \( R_2 \), and \( R_3 \), then back to the negative terminal. ### Solution 1. **Calculate Total Resistance**: The total resistance \( R_t \) for resistors in series is the sum of their resistances: \[ R_t = R_1 + R_2 + R_3 = 220 \, \Omega + 470 \, \Omega + 1000 \, \Omega = 1690 \, \Omega \] 2. **Determine the Current \( I \)**: Using Ohm's Law, \( V = IR \), the current \( I \) in the circuit is given by: \[ I = \frac{V_s}{R_t} = \frac{15 \, \text{V}}{1690 \, \Omega} \approx 0.00888 \, \text{A} \, \text{(or 8.88 mA)} \] 3. **Calculate the Voltage Across Each Resistor**: - **Voltage across \( R_1 \)**: \[ V_1 = I \times R_1 = 0.00888 \, \text{A} \times 220 \, \Omega = 1.9536 \, \text{V} \]
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