Determine the total resistance of the circuit, given: R₁ = 145 Q, R₂ = 164 Q, and R³ = 133 0 Ω (Round the FINAL answer to two decimal places.) E₁ R₁ ww R₂ R₂ www
Determine the total resistance of the circuit, given: R₁ = 145 Q, R₂ = 164 Q, and R³ = 133 0 Ω (Round the FINAL answer to two decimal places.) E₁ R₁ ww R₂ R₂ www
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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![**Problem: Calculate Total Resistance in a Parallel Circuit**
**Question:**
Determine the total resistance of the circuit, given:
\( R_1 = 145 \, \Omega, \, R_2 = 164 \, \Omega, \, \text{and} \, R_3 = 133 \, \Omega \)
(Round the FINAL answer to two decimal places.)
**Diagram Description:**
The circuit diagram shows a battery labeled \( E_T \) connected to three resistors in parallel configuration. The three resistors are labeled \( R_1 \), \( R_2 \), and \( R_3 \).
**Solution:**
1. **Understand the Formula:**
For resistors in parallel, the total resistance \( R_T \) is calculated using the formula:
\[
\frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}
\]
2. **Substitute Values:**
\[
\frac{1}{R_T} = \frac{1}{145} + \frac{1}{164} + \frac{1}{133}
\]
3. **Calculate Each Term:**
- \(\frac{1}{145} = 0.00690\)
- \(\frac{1}{164} = 0.00610\)
- \(\frac{1}{133} = 0.00752\)
4. **Find the Sum:**
\[
\frac{1}{R_T} = 0.00690 + 0.00610 + 0.00752 = 0.02052
\]
5. **Calculate \( R_T \):**
\[
R_T = \frac{1}{0.02052} \approx 48.74 \, \Omega
\]
**Final Answer:**
The total resistance of the circuit is approximately \( R_T = 48.74 \, \Omega \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe9163f72-9cb9-47ec-9932-aa32cb69a25b%2Fad11015f-2db3-4cd3-af62-2f17b6d34990%2F7di0ttk_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem: Calculate Total Resistance in a Parallel Circuit**
**Question:**
Determine the total resistance of the circuit, given:
\( R_1 = 145 \, \Omega, \, R_2 = 164 \, \Omega, \, \text{and} \, R_3 = 133 \, \Omega \)
(Round the FINAL answer to two decimal places.)
**Diagram Description:**
The circuit diagram shows a battery labeled \( E_T \) connected to three resistors in parallel configuration. The three resistors are labeled \( R_1 \), \( R_2 \), and \( R_3 \).
**Solution:**
1. **Understand the Formula:**
For resistors in parallel, the total resistance \( R_T \) is calculated using the formula:
\[
\frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}
\]
2. **Substitute Values:**
\[
\frac{1}{R_T} = \frac{1}{145} + \frac{1}{164} + \frac{1}{133}
\]
3. **Calculate Each Term:**
- \(\frac{1}{145} = 0.00690\)
- \(\frac{1}{164} = 0.00610\)
- \(\frac{1}{133} = 0.00752\)
4. **Find the Sum:**
\[
\frac{1}{R_T} = 0.00690 + 0.00610 + 0.00752 = 0.02052
\]
5. **Calculate \( R_T \):**
\[
R_T = \frac{1}{0.02052} \approx 48.74 \, \Omega
\]
**Final Answer:**
The total resistance of the circuit is approximately \( R_T = 48.74 \, \Omega \).
Expert Solution
Step 1: Equivalent resistance
The question is about finding equivalent resistance seen from the source.
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