Spring 2018
Equivalent Resistance
Find the Equivalent Resistance between two terminals
Learn It!
Pre-Requisite Knowledge
Equivalent Resistance
Find the Equivalent Resistance across terminals A & B and C & B
\( \begin{equation} a. R_{ab} = 8 k\Omega, R_{bc} = 4 k\Omega \\ b. R_{ab} = 4 k\Omega, R_{bc} = 8 k\Omega \\ c. R_{ab} = 4 k\Omega, R_{bc} = 3 k\Omega \\ d. R_{ab} = 3 k\Omega, R_{bc} = 8 k\Omega \\ e. R_{ab} = 3 k\Omega, R_{bc} = 3 k\Omega \end{equation} \)
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.
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
Transform both circuits
Fully Transformed
Part 2
Compute the Equivalent Resistance Using Formulas
Circuit AB is two 2-resistor series configurations in parallel with each other.
Circuit BC is a 3-resistor series in parallel with a single resistor.
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.