Equivalent Resistance Between Terminals
Fall 2018
Equivalent Resistance
Find the Equivalent Resistance between two terminals
Learn It!
Pre-Requisite Knowledge
Goal
Equivalent Resistance
Find the Equivalent Resistance across terminals A & B and C & B
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\( \begin{equation} a. R_{ab} = 8 k\Omega, R_{bc} = 4 k\Omega \\ b. R_{ab} = 4 k\Omega, R_{bc} = 8 k\Omega \\ c. R_{ab} = 4 k\Omega, R_{bc} = 3 k\Omega \\ d. R_{ab} = 3 k\Omega, R_{bc} = 8 k\Omega \\ e. R_{ab} = 3 k\Omega, R_{bc} = 3 k\Omega \end{equation} \)
Part 1
Reshape Both Circuits
The statement of the problem is straightforward, find the equivalent resistance. but The question seems at first a little absurd. It's the same resistors, why should the resistance be different?

It turns out they will be very different.
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We start with two circuits that look very similar. I'll be refering to "Circuit AB" and "Circuit BC" to label the left and right circuits, respectively
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1A
Transform both circuits
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Fully Transformed
Part 2
Compute the Equivalent Resistance Using Formulas
\[R_{ab}=(R+R)||(R+R)\]
Circuit AB is two 2-resistor series configurations in parallel with each other.
\[R_{bc}=(R+R+R)||(R)\]
Circuit BC is a 3-resistor series in parallel with a single resistor.
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2A
Reduce the circuits with series and parallel
\begin{aligned} R_{ab}&=\dfrac{1}{ \dfrac{2}{2R}}=R&=4 \\ R_{bc}&=\dfrac{1}{ \dfrac{4}{3R}}= \dfrac{3}{4}R&=3 \end{aligned}
Simplify fractions.
\begin{align} R_{ab}&=4 k\Omega \\ R_{bc}&=3 k\Omega \end{align}
Final Answer
Equivalent resistance is not only a property of the resistor network, but also of what points you measure between.