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Chapter 25: Problem 24

You have a \(1.0-\Omega,\) a \(2.0-\Omega,\) and a \(3.0-\Omega\) resistor. What equivalent resistances can you form using all three?

Short Answer

Expert verified
The equivalent resistances you can form using all three resistors are \( 6.0-惟 \) for the series configuration and approximately \( 0.55-惟 \) for the parallel configuration.

Step by step solution

01

Calculate Equivalent Resistance in Series

In a series configuration, the equivalent resistance \( R_{eq} \) is the sum of the individual resistances. Here, all three resistors are in series which means you just have to add the resistance values together: \( R_{eq-series} = R_1 + R_2 + R_3 = 1.0-惟 + 2.0-惟 + 3.0-惟 = 6.0-惟 \).
02

Calculate Equivalent Resistance in Parallel

In a parallel configuration, the reciprocals of the individual resistances add up to give the reciprocal of the equivalent resistance. So, the equivalent resistance \( R_{eq} \) is given as \( 1/R_{eq-parallel} = 1/R_1 + 1/R_2 + 1/R_3 = 1/(1.0-惟) + 1/(2.0-惟) + 1/(3.0-惟) \). Solve this equation to find the equivalent resistance in parallel.
03

Solve for the Equivalent Resistance in Parallel

To solve the equation from the second step, first find the sum of the reciprocals of resistance values: \( 1/R_{eq-parallel} = 1.0 + 0.5 + 0.33 = 1.83 \). Then take the reciprocal of this sum to find the equivalent resistance in parallel: \( R_{eq-parallel} = 1/1.83 鈮� 0.55-惟 \).

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