# How do you calculate the total resistance of a parallel circuit?

Apr 14, 2014

Use the resistance formula:

Example:

You have 4 resistors all connected in parallel. R1 and R2 each have a resistance of 4 ohms, R3 and R4 each have a resistance of 8 ohms. What is the total resistance?

$\frac{1}{\text{Rp}}$ = $\frac{1}{\text{R1}}$ + $\frac{1}{\text{R2}}$ + $\frac{1}{\text{R3}}$ + $\frac{1}{\text{R4}}$

$\frac{1}{\text{Rp}}$ = $\frac{1}{4}$ + $\frac{1}{4}$ + $\frac{1}{8}$ + $\frac{1}{8}$

(Find a common denominator)

$\frac{1}{\text{Rp}}$ = $\frac{2}{8}$ + $\frac{2}{8}$ + $\frac{1}{8}$ + $\frac{1}{8}$

$\frac{1}{\text{Rp}}$ = $\frac{6}{8}$

(Rp is the reciprocal of this)

Rp = $\frac{8}{6}$ = 1.33 ohms