College Physics
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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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Find the total resistance of the combination of resistors shown in the figure below. (R1 = 23.0 µΩ, R2 = 9.20 µΩ, and R3 = 0.300 µΩ.)
![The diagram illustrates a simple electrical circuit featuring three resistors: \( R_1 \), \( R_2 \), and \( R_3 \). Resistors \( R_1 \) and \( R_2 \) are arranged in parallel, and this parallel combination is connected in series with resistor \( R_3 \).
**Explanation of the Circuit:**
- **Parallel Resistors (\( R_1 \) and \( R_2 \)):**
- When resistors are in parallel, the total or equivalent resistance (\( R_{parallel} \)) is calculated using the formula:
\[
\frac{1}{R_{parallel}} = \frac{1}{R_1} + \frac{1}{R_2}
\]
This results in a lower equivalent resistance than the smallest individual resistor, as the current can flow through multiple paths.
- **Series Connection (with \( R_3 \)):**
- The equivalent resistance of the entire circuit is calculated by adding the resistance of \( R_3 \) to the equivalent resistance of the parallel combination:
\[
R_{total} = R_{parallel} + R_3
\]
Such configurations are commonly used in circuit design to achieve desired resistance values and current distribution. The series-parallel arrangement leverages both types of connections, achieving specific functionalities in electronic circuits.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa40285d1-fda7-4887-8299-84d11ca408ec%2Fcca0404d-1eca-41ce-b4e6-ebe098e71833%2F4kth5sq_processed.gif&w=3840&q=75)
Transcribed Image Text:The diagram illustrates a simple electrical circuit featuring three resistors: \( R_1 \), \( R_2 \), and \( R_3 \). Resistors \( R_1 \) and \( R_2 \) are arranged in parallel, and this parallel combination is connected in series with resistor \( R_3 \).
**Explanation of the Circuit:**
- **Parallel Resistors (\( R_1 \) and \( R_2 \)):**
- When resistors are in parallel, the total or equivalent resistance (\( R_{parallel} \)) is calculated using the formula:
\[
\frac{1}{R_{parallel}} = \frac{1}{R_1} + \frac{1}{R_2}
\]
This results in a lower equivalent resistance than the smallest individual resistor, as the current can flow through multiple paths.
- **Series Connection (with \( R_3 \)):**
- The equivalent resistance of the entire circuit is calculated by adding the resistance of \( R_3 \) to the equivalent resistance of the parallel combination:
\[
R_{total} = R_{parallel} + R_3
\]
Such configurations are commonly used in circuit design to achieve desired resistance values and current distribution. The series-parallel arrangement leverages both types of connections, achieving specific functionalities in electronic circuits.
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