If the total resistance of the circuit is 136 ohms, determine the value of R₁, given: R₁ . = 136 Q, R₂ = 34 Q, R₂ = 20 Q, and R₁ = 140 = 2 E₁ R₁ R₂ R₂ R₂ M www
If the total resistance of the circuit is 136 ohms, determine the value of R₁, given: R₁ . = 136 Q, R₂ = 34 Q, R₂ = 20 Q, and R₁ = 140 = 2 E₁ R₁ R₂ R₂ R₂ M www
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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Question
![**Problem Statement:**
If the total resistance of the circuit is 136 ohms, determine the value of \( R_1 \), given:
- \( R_T = 136 \, \Omega \)
- \( R_2 = 34 \, \Omega \)
- \( R_3 = 20 \, \Omega \)
- \( R_4 = 14 \, \Omega \)
**Circuit Diagram Explanation:**
The circuit consists of a simple series setup with a total of four resistors and a power source. The resistors are labeled as \( R_1 \), \( R_2 \), \( R_3 \), and \( R_4 \). The power source is labeled as \( E_T \).
- **Resistors:**
- \( R_1 \) is the resistor whose resistance value needs to be determined. It is connected directly to the power source in series with the other resistors.
- \( R_2 = 34 \, \Omega \)
- \( R_3 = 20 \, \Omega \)
- \( R_4 = 14 \, \Omega \)
- **Power Source:**
- Indicated by the symbol \( E_T \), placed on the left side of the circuit diagram, with positive and negative terminals marked.
**Calculating \( R_1 \):**
In a series circuit, the total resistance \( R_T \) is the sum of all individual resistances:
\[ R_T = R_1 + R_2 + R_3 + R_4 \]
Given:
\[ R_T = 136 \, \Omega \]
Substitute the known values:
\[ 136 \, \Omega = R_1 + 34 \, \Omega + 20 \, \Omega + 14 \, \Omega \]
Solving for \( R_1 \):
\[ R_1 = 136 \, \Omega - (34 \, \Omega + 20 \, \Omega + 14 \, \Omega) \]
\[ R_1 = 136 \, \Omega - 68 \, \Omega \]
\[ R_1 = 68 \, \Omega \]
Hence, the resistance of \( R_1 \) is 68 ohms.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3864bbe0-e2c9-459a-9920-261a79870337%2Fc66ca5a4-746b-4300-9d0b-c623dca1da06%2F4ioi24o_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
If the total resistance of the circuit is 136 ohms, determine the value of \( R_1 \), given:
- \( R_T = 136 \, \Omega \)
- \( R_2 = 34 \, \Omega \)
- \( R_3 = 20 \, \Omega \)
- \( R_4 = 14 \, \Omega \)
**Circuit Diagram Explanation:**
The circuit consists of a simple series setup with a total of four resistors and a power source. The resistors are labeled as \( R_1 \), \( R_2 \), \( R_3 \), and \( R_4 \). The power source is labeled as \( E_T \).
- **Resistors:**
- \( R_1 \) is the resistor whose resistance value needs to be determined. It is connected directly to the power source in series with the other resistors.
- \( R_2 = 34 \, \Omega \)
- \( R_3 = 20 \, \Omega \)
- \( R_4 = 14 \, \Omega \)
- **Power Source:**
- Indicated by the symbol \( E_T \), placed on the left side of the circuit diagram, with positive and negative terminals marked.
**Calculating \( R_1 \):**
In a series circuit, the total resistance \( R_T \) is the sum of all individual resistances:
\[ R_T = R_1 + R_2 + R_3 + R_4 \]
Given:
\[ R_T = 136 \, \Omega \]
Substitute the known values:
\[ 136 \, \Omega = R_1 + 34 \, \Omega + 20 \, \Omega + 14 \, \Omega \]
Solving for \( R_1 \):
\[ R_1 = 136 \, \Omega - (34 \, \Omega + 20 \, \Omega + 14 \, \Omega) \]
\[ R_1 = 136 \, \Omega - 68 \, \Omega \]
\[ R_1 = 68 \, \Omega \]
Hence, the resistance of \( R_1 \) is 68 ohms.
Expert Solution
Step 1: Equivalent resistance
The question is about finding the resistor value R1.
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