Two resistors connected in series have an equivalent resistance of 781.3 . When they are connected in parallel, their equivalent resistance is 154.9 2. Find the resistance of each resistor. 2 (small resistance) (large resistance)
Two resistors connected in series have an equivalent resistance of 781.3 . When they are connected in parallel, their equivalent resistance is 154.9 2. Find the resistance of each resistor. 2 (small resistance) (large resistance)
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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![**Problem: Calculating Individual Resistor Values**
Two resistors connected in series have an equivalent resistance of **781.3 Ω**. When they are connected in parallel, their equivalent resistance is **154.9 Ω**. Find the resistance of each resistor.
- \[ \, \Omega \] (small resistance)
- \[ \, \Omega \] (large resistance)
**Explanation:**
To solve this, let the resistances be \( R_1 \) and \( R_2 \).
1. **Series Connection:**
- The equivalent resistance (\( R_s \)) is the sum of the resistances:
\[
R_s = R_1 + R_2 = 781.3
\]
2. **Parallel Connection:**
- The equivalent resistance (\( R_p \)) is given by:
\[
\frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2}
\]
- Which can be rearranged to:
\[
R_p = \frac{R_1 \times R_2}{R_1 + R_2}
\]
- Given \( R_p = 154.9 \):
\[
\frac{R_1 \times R_2}{781.3} = 154.9
\]
\[
R_1 \times R_2 = 154.9 \times 781.3
\]
You can solve these equations simultaneously to find \( R_1 \) and \( R_2 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F99e37c92-095a-4cae-adf6-01aeaaa5668c%2F2ab1a9ad-2072-458c-ba25-38b323cdee32%2Fngerfhb_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem: Calculating Individual Resistor Values**
Two resistors connected in series have an equivalent resistance of **781.3 Ω**. When they are connected in parallel, their equivalent resistance is **154.9 Ω**. Find the resistance of each resistor.
- \[ \, \Omega \] (small resistance)
- \[ \, \Omega \] (large resistance)
**Explanation:**
To solve this, let the resistances be \( R_1 \) and \( R_2 \).
1. **Series Connection:**
- The equivalent resistance (\( R_s \)) is the sum of the resistances:
\[
R_s = R_1 + R_2 = 781.3
\]
2. **Parallel Connection:**
- The equivalent resistance (\( R_p \)) is given by:
\[
\frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2}
\]
- Which can be rearranged to:
\[
R_p = \frac{R_1 \times R_2}{R_1 + R_2}
\]
- Given \( R_p = 154.9 \):
\[
\frac{R_1 \times R_2}{781.3} = 154.9
\]
\[
R_1 \times R_2 = 154.9 \times 781.3
\]
You can solve these equations simultaneously to find \( R_1 \) and \( R_2 \).
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