Showing posts with label circuits. Show all posts
Showing posts with label circuits. Show all posts

Friday, March 23, 2012

Two current divider rules

Wikipedia has the following current divider rule

$$I_X = \frac{R_T}{R_X + R_T} \times I_T$$

where as certain websites have the following rule:

$$I_X = \frac{R_{total}}{R_X} \times I_T$$

where

$$\frac{1}{R_{total}} = \frac{1}{R_X} + \frac{1}{R_T}$$

for two resistors, this simplifies to

$$R_{total} = \frac{R_X \times R_T}{R_X + R_T}$$

These two rules are equal:

\begin{align}
I_X &= I_T \times \frac{R_{total}}{R_X} \\
&= I_T \times R_{total} \times \frac{1}{R_X} \\
&= I_T \times \frac{R_X \times R_T}{R_X + R_T} \times \frac{1}{R_X} \\
&= I_T \times \frac{R_T}{R_X + R_T}
\end{align}