In the circuit shown below, determine the current in the circuit. How much power is dissipated by each resistor in the figure? R₁ = 120 9.0 V R₂= = 15 Ω wwwwww
In the circuit shown below, determine the current in the circuit. How much power is dissipated by each resistor in the figure? R₁ = 120 9.0 V R₂= = 15 Ω wwwwww
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)...
Related questions
Question
![**Determine Current and Power in Series Circuit**
**Problem Overview:**
In the circuit shown below, determine the current in the circuit. How much power is dissipated by each resistor in the figure?
**Circuit Diagram:**
The circuit consists of a series connection with the following components:
- A voltage source of 9.0 volts (V).
- Two resistors:
- \( R_1 \) with a resistance of 12 ohms (Ω).
- \( R_2 \) with a resistance of 15 ohms (Ω).
**Analysis:**
1. **Total Resistance in the Circuit:**
Since the resistors are in series, the total resistance \( R_t \) is the sum of the resistances:
\[
R_t = R_1 + R_2 = 12 \, \Omega + 15 \, \Omega = 27 \, \Omega
\]
2. **Current in the Circuit:**
Using Ohm's Law to determine the current \( I \) in the circuit:
\[
I = \frac{V}{R_t} = \frac{9.0 \, \text{V}}{27 \, \Omega} = 0.33 \, \text{A} \, (\text{or } \frac{1}{3} \, \text{A})
\]
3. **Power Dissipated by Each Resistor:**
- For \( R_1 \):
\[
P_1 = I^2 \times R_1 = (0.33 \, \text{A})^2 \times 12 \, \Omega = 0.11 \, \text{W}
\]
- For \( R_2 \):
\[
P_2 = I^2 \times R_2 = (0.33 \, \text{A})^2 \times 15 \, \Omega = 0.165 \, \text{W}
\]
**Conclusion:**
The current in the circuit is 0.33 A. The power dissipated by resistor \( R_1 \) is 0.11 W, and the power dissipated by resistor \( R_2 \) is 0.165 W.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4a6e4794-5644-431d-9e96-b37fbaf0b60a%2F13ea38f3-ca6d-45f1-a1eb-dcb3f1302ad7%2Fqrxuswt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Determine Current and Power in Series Circuit**
**Problem Overview:**
In the circuit shown below, determine the current in the circuit. How much power is dissipated by each resistor in the figure?
**Circuit Diagram:**
The circuit consists of a series connection with the following components:
- A voltage source of 9.0 volts (V).
- Two resistors:
- \( R_1 \) with a resistance of 12 ohms (Ω).
- \( R_2 \) with a resistance of 15 ohms (Ω).
**Analysis:**
1. **Total Resistance in the Circuit:**
Since the resistors are in series, the total resistance \( R_t \) is the sum of the resistances:
\[
R_t = R_1 + R_2 = 12 \, \Omega + 15 \, \Omega = 27 \, \Omega
\]
2. **Current in the Circuit:**
Using Ohm's Law to determine the current \( I \) in the circuit:
\[
I = \frac{V}{R_t} = \frac{9.0 \, \text{V}}{27 \, \Omega} = 0.33 \, \text{A} \, (\text{or } \frac{1}{3} \, \text{A})
\]
3. **Power Dissipated by Each Resistor:**
- For \( R_1 \):
\[
P_1 = I^2 \times R_1 = (0.33 \, \text{A})^2 \times 12 \, \Omega = 0.11 \, \text{W}
\]
- For \( R_2 \):
\[
P_2 = I^2 \times R_2 = (0.33 \, \text{A})^2 \times 15 \, \Omega = 0.165 \, \text{W}
\]
**Conclusion:**
The current in the circuit is 0.33 A. The power dissipated by resistor \( R_1 \) is 0.11 W, and the power dissipated by resistor \( R_2 \) is 0.165 W.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 3 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Recommended textbooks for you
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON