DC Circuits: Calculating Total Resistance

Calculating for the total resistance across series and parallel connections is not the same.

Series Resistance

$R_T = R_1+R_2+R_3$

See an example here.

Parallel Resistance

$R_T = \frac{1}{\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}}$

$R_T = \frac{R_1R_2R_3}{R_1+R_2+R_3}$

An example will be available tomorrow
Update: Example here.

Mixed Resistance (Series and Parallel)
Complexity arises when there comes many resistors in a circuit connected together either in series or in parallel. In that case, analyze carefully.

Notice that R2 and R1 are connected in parallel to each other. Thus,

$R_{23} = \frac{R_2R_3}{R_2+R_3}$

Now, we will have this simplified circuit:

This simplified circuit has R1 connected in series with R23, thus,

$R_T = R_{123} = \frac{R_1R_{23}}{R_1+R_{23}}$

There are circuits much more complex than these examples. Start with these to practice with your circuit analysis.

DC Circuits: Calculating Total Resistance

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