An engineer fashions an 3.9-k equivalent resistor from a parallel combination of 4 equal- value resistors. What is the resistance (in k) of each individual resistor?
An engineer fashions an 3.9-k equivalent resistor from a parallel combination of 4 equal- value resistors. What is the resistance (in k) of each individual resistor?
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Question
![**Problem:**
An engineer fashions a 3.9-kΩ equivalent resistor from a parallel combination of 4 equal-value resistors. What is the resistance (in kΩ) of each individual resistor?
**Solution Explanation:**
When resistors are combined in parallel, the reciprocal of the total or equivalent resistance (\(R_{eq}\)) is the sum of the reciprocals of each individual resistance (\(R\)).
For \(n\) equal resistors in parallel, the equation is:
\[
\frac{1}{R_{eq}} = \frac{n}{R}
\]
Given:
- \(R_{eq} = 3.9 \, \text{kΩ}\)
- \(n = 4\)
We need to find the resistance \(R\) of each resistor.
From the formula, we have:
\[
\frac{1}{3.9} = \frac{4}{R}
\]
Solving for \(R\):
\[
R = \frac{4}{\frac{1}{3.9}}
\]
\[
R = 4 \times 3.9
\]
\[
R = 15.6 \, \text{kΩ}
\]
Therefore, the resistance of each individual resistor is 15.6 kΩ.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F047a7e6a-f025-4b5b-ab83-4ffe14f69253%2Fd9af79d2-9944-48e0-b10d-45d54666cddd%2Ff8fk6qb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem:**
An engineer fashions a 3.9-kΩ equivalent resistor from a parallel combination of 4 equal-value resistors. What is the resistance (in kΩ) of each individual resistor?
**Solution Explanation:**
When resistors are combined in parallel, the reciprocal of the total or equivalent resistance (\(R_{eq}\)) is the sum of the reciprocals of each individual resistance (\(R\)).
For \(n\) equal resistors in parallel, the equation is:
\[
\frac{1}{R_{eq}} = \frac{n}{R}
\]
Given:
- \(R_{eq} = 3.9 \, \text{kΩ}\)
- \(n = 4\)
We need to find the resistance \(R\) of each resistor.
From the formula, we have:
\[
\frac{1}{3.9} = \frac{4}{R}
\]
Solving for \(R\):
\[
R = \frac{4}{\frac{1}{3.9}}
\]
\[
R = 4 \times 3.9
\]
\[
R = 15.6 \, \text{kΩ}
\]
Therefore, the resistance of each individual resistor is 15.6 kΩ.
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