The four resistors in the figure have an equivalent resistance of 122. The resistances are as follows: R¡ = 8.02, R, = 4.02, and R3 - 4.02. Calculate the value of R, . min R, - Ω
The four resistors in the figure have an equivalent resistance of 122. The resistances are as follows: R¡ = 8.02, R, = 4.02, and R3 - 4.02. Calculate the value of R, . min R, - Ω
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 Description:**
The four resistors in the figure have an equivalent resistance of 12 Ω. The resistances are as follows:
- \( R_1 = 8.0 \, \Omega \)
- \( R_2 = 4.0 \, \Omega \)
- \( R_3 = 4.0 \, \Omega \)
Calculate the value of \( R_x \).
**Diagram Explanation:**
The diagram on the right shows a circuit with four resistors:
1. \( R_1 \) and \( R_x \) are connected in parallel.
2. The combination of \( R_1 \) and \( R_x \) is in series with \( R_2 \) and \( R_3 \).
**Solution Steps:**
1. **Parallel Combination:**
The equivalent resistance \( R_p \) of \( R_1 \) and \( R_x \) in parallel is given by:
\[
\frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_x}
\]
2. **Series Combination:**
The total equivalent resistance \( R_{eq} \) is:
\[
R_{eq} = R_p + R_2 + R_3
\]
Given \( R_{eq} = 12 \, \Omega \), substitute the known values:
\[
12 = R_p + 4 + 4
\]
\[
12 = R_p + 8
\]
\[
R_p = 4 \, \Omega
\]
3. **Calculate \( R_x \):**
Using the parallel resistance formula for \( R_p = 4 \, \Omega \):
\[
\frac{1}{4} = \frac{1}{8} + \frac{1}{R_x}
\]
\[
\frac{1}{R_x} = \frac{1}{4} - \frac{1}{8}
\]
\[
\frac{1}{R_x} = \frac{2}{8} - \frac{1}{8}
\]
\[
\frac{1}{R_x} = \frac{1}{8}
\]
\[
R_x =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0cf0a857-a468-42cd-8d56-fd83f38d342e%2Fb09a2a3c-e150-425e-a97b-59e4b7965c05%2F81pd0ql_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Description:**
The four resistors in the figure have an equivalent resistance of 12 Ω. The resistances are as follows:
- \( R_1 = 8.0 \, \Omega \)
- \( R_2 = 4.0 \, \Omega \)
- \( R_3 = 4.0 \, \Omega \)
Calculate the value of \( R_x \).
**Diagram Explanation:**
The diagram on the right shows a circuit with four resistors:
1. \( R_1 \) and \( R_x \) are connected in parallel.
2. The combination of \( R_1 \) and \( R_x \) is in series with \( R_2 \) and \( R_3 \).
**Solution Steps:**
1. **Parallel Combination:**
The equivalent resistance \( R_p \) of \( R_1 \) and \( R_x \) in parallel is given by:
\[
\frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_x}
\]
2. **Series Combination:**
The total equivalent resistance \( R_{eq} \) is:
\[
R_{eq} = R_p + R_2 + R_3
\]
Given \( R_{eq} = 12 \, \Omega \), substitute the known values:
\[
12 = R_p + 4 + 4
\]
\[
12 = R_p + 8
\]
\[
R_p = 4 \, \Omega
\]
3. **Calculate \( R_x \):**
Using the parallel resistance formula for \( R_p = 4 \, \Omega \):
\[
\frac{1}{4} = \frac{1}{8} + \frac{1}{R_x}
\]
\[
\frac{1}{R_x} = \frac{1}{4} - \frac{1}{8}
\]
\[
\frac{1}{R_x} = \frac{2}{8} - \frac{1}{8}
\]
\[
\frac{1}{R_x} = \frac{1}{8}
\]
\[
R_x =
Expert Solution
Step 1
Given Data
Resistance of the resistors are
Equivalent resistance of the circuit is
Concept
In the given circuit and are connected in parallel combination and equivalent resistance of these two resistors is connected in series with and .
Formula to be used
where is the equivalent resistance of the parallel combination of and
is the equivalent resistance of the circuit.
Step by step
Solved in 3 steps
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