Question

three components in a parallel circuit have individual resistances of $r_1$, $r_2$, and $r_3$.
what formula can you use to determine the total resistance of the circuit?
$r = \frac{1}{r_1} + \frac{1}{r_2} + \frac{1}{r_3}$
$r = r_1 + r_2 + r_3$
$\frac{1}{r} = r_1 + r_2 + r_3$
$\frac{1}{r} = \frac{1}{r_1} + \frac{1}{r_2} + \frac{1}{r_3}$

Explanation:

Step1: Recall parallel resistance rule

For resistors in parallel, the reciprocal of total resistance equals the sum of reciprocals of individual resistances.

Step2: Match to given options

The formula for 3 resistors $r_1, r_2, r_3$ in parallel is $\frac{1}{R} = \frac{1}{r_1} + \frac{1}{r_2} + \frac{1}{r_3}$.

Answer:

$\boldsymbol{\frac{1}{R} = \frac{1}{r_1} + \frac{1}{r_2} + \frac{1}{r_3}}$ (the last option)