﻿ 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
$$$a. R_{ab} = 8 k\Omega, R_{bc} = 4 k\Omega \\ b. R_{ab} = 4 k\Omega, R_{bc} = 8 k\Omega \\ c. R_{ab} = 4 k\Omega, R_{bc} = 3 k\Omega \\ d. R_{ab} = 3 k\Omega, R_{bc} = 8 k\Omega \\ e. R_{ab} = 3 k\Omega, R_{bc} = 3 k\Omega$$$
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
+
1A
Transform both circuits
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.
+
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}