Example: Calculating resistance
Calculate the resistance of the two resistors in parallel.
Answer
\(\frac{1}{R}=\frac{1}{R}_{1}+\frac{1}{R}_{2}\)
R1 = \({8}\Omega\)
R2 = \({8}\Omega\)
\(\frac{1}{R}=\frac{1}{8} + \frac{1}{8}\)
\(\frac{1}{R}=\frac{2}{8}\)
R = \(\frac{8}{2}\)
R = \({4}\Omega\)
The total resistance of the two resistors in parallel is \({4}\Omega\).
When two equal resistors are connected in parallel, the total resistance is always equal to half the resistance of one of the resistors.
This only works for two equal resistors connected in parallel and should only be used to check your answer.
Example
Calculate the resistance of the two resistors in parallel.
Answer
\(\frac{1}{R}=\frac{1}{R}_{1}+\frac{1}{R}_{2}\)
R1 = \({50}\Omega\)
R2 = \({50}\Omega\)
\(\frac{1}{R}=\frac{1}{50} +\frac{1}{50}\)
\(\frac{1}{R}=\frac{2}{50}\)
R = \(\frac{50}{2}\)
R = \({25}\Omega\)
The total resistance of the two resistors in parallel is \({25}\Omega\).
(Quick check: when two equal resistors are calculated in parallel, the total resistance is always equal to half the resistance of one of the resistors. Half of \({50}\Omega\) is \({25}\Omega\) and so the answer is correct.)