Given the parallel circuit presented below calculate the Equivalent Resistance Req when R1=400; R2=400 and R3=200. The Voltage of the battery is unknown.
Given the parallel circuit presented below calculate the Equivalent Resistance Req when R1=400; R2=400 and R3=200. The Voltage of the battery is unknown.
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11th Edition
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Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
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![**Instruction:**
Given the parallel circuit presented below, calculate the Equivalent Resistance (Req) when R1=40Ω, R2=40Ω, and R3=20Ω. The Voltage of the battery is unknown.
**Diagram Explanation:**
The diagram depicts a parallel circuit connected to a battery. The circuit consists of three resistors labeled R1, R2, and R3.
1. **Battery:** Positioned on the left side, symbolizing the power source for the circuit.
2. **Resistors:**
- **R1:** Positioned first, has a resistance value of 40Ω.
- **R2:** Positioned second, has a resistance value of 40Ω.
- **R3:** Positioned third, has a resistance value of 20Ω.
The resistors are connected in parallel, meaning each one is directly connected across the same voltage source (the battery).
**Calculating Equivalent Resistance in Parallel:**
For resistors in parallel, the formula for equivalent resistance (Req) is given by:
\[ \frac{1}{Req} = \frac{1}{R1} + \frac{1}{R2} + \frac{1}{R3} \]
Substituting in the given values:
\[ \frac{1}{Req} = \frac{1}{40} + \frac{1}{40} + \frac{1}{20} \]
Calculating each term:
\[ \frac{1}{40} = 0.025 \]
\[ \frac{1}{40} = 0.025 \]
\[ \frac{1}{20} = 0.05 \]
Adding these reciprocals:
\[ \frac{1}{Req} = 0.025 + 0.025 + 0.05 = 0.1 \]
Therefore, the equivalent resistance is:
\[ Req = \frac{1}{0.1} = 10Ω \]
The equivalent resistance of the parallel circuit is 10Ω.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F10fe2450-1369-43ac-b245-d62a2482d3d1%2Fb130ce14-acb3-4070-a8f0-a290e72fba78%2F4wu6uc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Instruction:**
Given the parallel circuit presented below, calculate the Equivalent Resistance (Req) when R1=40Ω, R2=40Ω, and R3=20Ω. The Voltage of the battery is unknown.
**Diagram Explanation:**
The diagram depicts a parallel circuit connected to a battery. The circuit consists of three resistors labeled R1, R2, and R3.
1. **Battery:** Positioned on the left side, symbolizing the power source for the circuit.
2. **Resistors:**
- **R1:** Positioned first, has a resistance value of 40Ω.
- **R2:** Positioned second, has a resistance value of 40Ω.
- **R3:** Positioned third, has a resistance value of 20Ω.
The resistors are connected in parallel, meaning each one is directly connected across the same voltage source (the battery).
**Calculating Equivalent Resistance in Parallel:**
For resistors in parallel, the formula for equivalent resistance (Req) is given by:
\[ \frac{1}{Req} = \frac{1}{R1} + \frac{1}{R2} + \frac{1}{R3} \]
Substituting in the given values:
\[ \frac{1}{Req} = \frac{1}{40} + \frac{1}{40} + \frac{1}{20} \]
Calculating each term:
\[ \frac{1}{40} = 0.025 \]
\[ \frac{1}{40} = 0.025 \]
\[ \frac{1}{20} = 0.05 \]
Adding these reciprocals:
\[ \frac{1}{Req} = 0.025 + 0.025 + 0.05 = 0.1 \]
Therefore, the equivalent resistance is:
\[ Req = \frac{1}{0.1} = 10Ω \]
The equivalent resistance of the parallel circuit is 10Ω.
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