Q2: Find Req. for the circuit shown in the figure below? 1.5Ω Solution: ww Rea 1.52 1.50 ww ww ww
Q2: Find Req. for the circuit shown in the figure below? 1.5Ω Solution: ww Rea 1.52 1.50 ww ww ww
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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![**Q2: Find Req. for the circuit shown in the figure below?**
**Solution:**
The diagram shows a complex electrical circuit composed of several resistors. The resistors are arranged in a combination of series and parallel configurations.
- There is a 3Ω resistor connected in series at the top.
- Parallel to this 3Ω resistor, a combination of resistors is present: a 2Ω resistor and another branch that has two 2Ω resistors in parallel.
- The parallel branch connects to a 1.5Ω resistor on both sides, which further connects to a 1.5Ω resistor in series at the bottom.
To find \( R_{eq} \), or the equivalent resistance:
1. Calculate the equivalent resistance for the two 2Ω resistors in parallel:
\[
R_{parallel} = \frac{1}{\frac{1}{2} + \frac{1}{2}} = 1Ω
\]
2. This 1Ω resistance is in series with another 2Ω resistor (same branch), giving:
\[
R_{series} = 1Ω + 2Ω = 3Ω
\]
3. This resulting 3Ω is in parallel with the top 3Ω resistor:
\[
R_{combined} = \frac{1}{\frac{1}{3} + \frac{1}{3}} = 1.5Ω
\]
4. Add the series resistances along the bottom:
\[
R_{eq} = 1.5Ω + 1.5Ω = 3Ω
\]
The equivalent resistance of the circuit \( R_{eq} \) is 3Ω.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F199d58c4-213a-4e42-b645-d01318acf93a%2Ff33ddfd4-9ed8-4cfe-a4a5-4be0447dc971%2Fhgg3kk9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Q2: Find Req. for the circuit shown in the figure below?**
**Solution:**
The diagram shows a complex electrical circuit composed of several resistors. The resistors are arranged in a combination of series and parallel configurations.
- There is a 3Ω resistor connected in series at the top.
- Parallel to this 3Ω resistor, a combination of resistors is present: a 2Ω resistor and another branch that has two 2Ω resistors in parallel.
- The parallel branch connects to a 1.5Ω resistor on both sides, which further connects to a 1.5Ω resistor in series at the bottom.
To find \( R_{eq} \), or the equivalent resistance:
1. Calculate the equivalent resistance for the two 2Ω resistors in parallel:
\[
R_{parallel} = \frac{1}{\frac{1}{2} + \frac{1}{2}} = 1Ω
\]
2. This 1Ω resistance is in series with another 2Ω resistor (same branch), giving:
\[
R_{series} = 1Ω + 2Ω = 3Ω
\]
3. This resulting 3Ω is in parallel with the top 3Ω resistor:
\[
R_{combined} = \frac{1}{\frac{1}{3} + \frac{1}{3}} = 1.5Ω
\]
4. Add the series resistances along the bottom:
\[
R_{eq} = 1.5Ω + 1.5Ω = 3Ω
\]
The equivalent resistance of the circuit \( R_{eq} \) is 3Ω.
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