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. Battery R1 R2 R3
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. Battery R1 R2 R3
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![**Question #10**
Given the parallel circuit presented below, calculate the Equivalent Resistance \( R_{eq} \) when \( R_1 = 40\Omega \); \( R_2 = 40\Omega \), and \( R_3 = 20\Omega \). The Voltage of the battery is unknown.
**Diagram Explanation:**
The diagram shows a parallel circuit powered by a battery. The circuit consists of three resistors labeled \( R_1 \), \( R_2 \), and \( R_3 \).
- **Battery**: Depicted on the left, providing power to the circuit.
- **Resistors**: Arranged in parallel across the battery:
- \( R_1 = 40\Omega \)
- \( R_2 = 40\Omega \)
- \( R_3 = 20\Omega \)
**Equivalent Resistance Calculation**:
In a parallel circuit, the Equivalent Resistance (\( R_{eq} \)) can be calculated using the formula:
\[
\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}
\]
Substitute the values:
\[
\frac{1}{R_{eq}} = \frac{1}{40} + \frac{1}{40} + \frac{1}{20}
\]
Calculate each term:
\[
\frac{1}{R_{eq}} = \frac{1}{40} + \frac{1}{40} + \frac{1}{20} = \frac{1}{40} + \frac{1}{40} + \frac{2}{40} = \frac{4}{40} = \frac{1}{10}
\]
Therefore, the equivalent resistance is:
\[
R_{eq} = 10\Omega
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Transcribed Image Text:**Question #10**
Given the parallel circuit presented below, calculate the Equivalent Resistance \( R_{eq} \) when \( R_1 = 40\Omega \); \( R_2 = 40\Omega \), and \( R_3 = 20\Omega \). The Voltage of the battery is unknown.
**Diagram Explanation:**
The diagram shows a parallel circuit powered by a battery. The circuit consists of three resistors labeled \( R_1 \), \( R_2 \), and \( R_3 \).
- **Battery**: Depicted on the left, providing power to the circuit.
- **Resistors**: Arranged in parallel across the battery:
- \( R_1 = 40\Omega \)
- \( R_2 = 40\Omega \)
- \( R_3 = 20\Omega \)
**Equivalent Resistance Calculation**:
In a parallel circuit, the Equivalent Resistance (\( R_{eq} \)) can be calculated using the formula:
\[
\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}
\]
Substitute the values:
\[
\frac{1}{R_{eq}} = \frac{1}{40} + \frac{1}{40} + \frac{1}{20}
\]
Calculate each term:
\[
\frac{1}{R_{eq}} = \frac{1}{40} + \frac{1}{40} + \frac{1}{20} = \frac{1}{40} + \frac{1}{40} + \frac{2}{40} = \frac{4}{40} = \frac{1}{10}
\]
Therefore, the equivalent resistance is:
\[
R_{eq} = 10\Omega
\]
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