Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
Related questions
Question
![**Topic: Verifying Equivalent Equations in Electrical Circuits**
**Objective:**
Show ALL steps to verify the following equations are equivalent.
\[ E = Ir + IR \]
and
\[ I = \frac{E}{r+R} \]
**Steps to Verify the Equations:**
1. **Starting with the given equations:**
- Equation 1: \( E = Ir + IR \)
- Equation 2: \( I = \frac{E}{r+R} \)
2. **Manipulate Equation 1 to express \( I \):**
\[ E = I (r + R) \]
3. **Isolate \( I \) on one side of the equation:**
\[ I = \frac{E}{r + R} \]
4. **Compare the manipulated Equation 1 with Equation 2:**
- They are identical in form:
\[ I = \frac{E}{r+R} \]
This shows that both equations are equivalent.
### Explanation:
- **Equation 1** represents Ohm's Law as applied to a circuit with internal resistance \( r \) and external resistance \( R \).
- **Equation 2** is a reformulation of the same relationship, isolating the current \( I \) and showing it as a function of the total resistance \( r + R \).
By manipulating the first equation and deriving the second equation, we have demonstrated the equivalence of these two electrical principles, often used in analyzing simple circuits.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4fcdecb9-56df-4c9c-aece-60df7fbe5b7a%2F9fcf4e14-722d-4961-9032-ebf88ae8f717%2Fpopna8_processed.png&w=3840&q=75)
Transcribed Image Text:**Topic: Verifying Equivalent Equations in Electrical Circuits**
**Objective:**
Show ALL steps to verify the following equations are equivalent.
\[ E = Ir + IR \]
and
\[ I = \frac{E}{r+R} \]
**Steps to Verify the Equations:**
1. **Starting with the given equations:**
- Equation 1: \( E = Ir + IR \)
- Equation 2: \( I = \frac{E}{r+R} \)
2. **Manipulate Equation 1 to express \( I \):**
\[ E = I (r + R) \]
3. **Isolate \( I \) on one side of the equation:**
\[ I = \frac{E}{r + R} \]
4. **Compare the manipulated Equation 1 with Equation 2:**
- They are identical in form:
\[ I = \frac{E}{r+R} \]
This shows that both equations are equivalent.
### Explanation:
- **Equation 1** represents Ohm's Law as applied to a circuit with internal resistance \( r \) and external resistance \( R \).
- **Equation 2** is a reformulation of the same relationship, isolating the current \( I \) and showing it as a function of the total resistance \( r + R \).
By manipulating the first equation and deriving the second equation, we have demonstrated the equivalence of these two electrical principles, often used in analyzing simple circuits.
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
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education