In the 8Ω resistor, the current has the value of 0.50A. Find the value of the current in the 2Ω resistor. Note that knowing the battery voltage is not necessary to solve the problem. Answer choices: 4.5 A 2.2 A 6.4 A 9.5 A 0.75 A
In the 8Ω resistor, the current has the value of 0.50A. Find the value of the current in the 2Ω resistor. Note that knowing the battery voltage is not necessary to solve the problem. Answer choices: 4.5 A 2.2 A 6.4 A 9.5 A 0.75 A
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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Question
In the 8Ω resistor, the current has the value of 0.50A. Find the value of the current in the 2Ω resistor. Note that knowing the battery voltage is not necessary to solve the problem.
Answer choices:
4.5 A
2.2 A
6.4 A
9.5 A
0.75 A
![### Circuit Diagram Explanation
This diagram represents an electrical circuit containing multiple resistors and a power source. The circuit includes the following components and arrangements:
1. **Resistors in Parallel:**
- Two resistors, 16 Ω and 8 Ω, are connected in parallel.
- Another set of two resistors, 6 Ω and 2 Ω, are also connected in parallel.
2. **Resistor in Series:**
- A single resistor of 20 Ω is connected in series with the first parallel combination (16 Ω and 8 Ω).
3. **Power Source:**
- There is a power source indicated by a battery symbol placed horizontally between the two parallel combinations. The positive terminal is noted by a '+' sign.
### Analysis
- **Parallel Resistor Combination:**
- For the 16 Ω and 8 Ω resistors in parallel, the equivalent resistance \( R_1 \) can be calculated using the formula:
\[
\frac{1}{R_1} = \frac{1}{16} + \frac{1}{8}
\]
- For the 6 Ω and 2 Ω resistors in parallel, the equivalent resistance \( R_2 \) can be calculated using:
\[
\frac{1}{R_2} = \frac{1}{6} + \frac{1}{2}
\]
- **Series Resistor Combination:**
- The equivalent resistance of the parallel combination (16 Ω and 8 Ω) and the 20 Ω resistor is added together. The formula for series resistance \( R_3 \) is:
\[
R_3 = R_1 + 20
\]
### Practical Application
This circuit illustrates the principles of combining resistors in series and parallel configurations to find total resistance. Understanding such combinations is critical in calculating total current flow and voltage distribution in electrical circuits.
This type of analysis is foundational in electronics, physics education, and practical electrical engineering applications.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F73b12af7-3b36-49b3-b08b-77695dab16d2%2Fe52debd3-3be8-40bf-aaf4-6b31dea7e709%2F5tzpv6a_processed.png&w=3840&q=75)
Transcribed Image Text:### Circuit Diagram Explanation
This diagram represents an electrical circuit containing multiple resistors and a power source. The circuit includes the following components and arrangements:
1. **Resistors in Parallel:**
- Two resistors, 16 Ω and 8 Ω, are connected in parallel.
- Another set of two resistors, 6 Ω and 2 Ω, are also connected in parallel.
2. **Resistor in Series:**
- A single resistor of 20 Ω is connected in series with the first parallel combination (16 Ω and 8 Ω).
3. **Power Source:**
- There is a power source indicated by a battery symbol placed horizontally between the two parallel combinations. The positive terminal is noted by a '+' sign.
### Analysis
- **Parallel Resistor Combination:**
- For the 16 Ω and 8 Ω resistors in parallel, the equivalent resistance \( R_1 \) can be calculated using the formula:
\[
\frac{1}{R_1} = \frac{1}{16} + \frac{1}{8}
\]
- For the 6 Ω and 2 Ω resistors in parallel, the equivalent resistance \( R_2 \) can be calculated using:
\[
\frac{1}{R_2} = \frac{1}{6} + \frac{1}{2}
\]
- **Series Resistor Combination:**
- The equivalent resistance of the parallel combination (16 Ω and 8 Ω) and the 20 Ω resistor is added together. The formula for series resistance \( R_3 \) is:
\[
R_3 = R_1 + 20
\]
### Practical Application
This circuit illustrates the principles of combining resistors in series and parallel configurations to find total resistance. Understanding such combinations is critical in calculating total current flow and voltage distribution in electrical circuits.
This type of analysis is foundational in electronics, physics education, and practical electrical engineering applications.
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