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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**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.
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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