# Question #60982

Feb 13, 2017

$\frac{6}{11}$ Ohms

#### Explanation:

The total resistance, ${R}_{T}$, of a parallel set of $n$ resistors is

$\frac{1}{R} _ T = \Sigma \frac{1}{R} _ n \implies {R}_{T} = \frac{1}{\Sigma \frac{1}{R} _ n}$

Here we can see this as:

$\frac{1}{R} _ T = \frac{1}{1} + \frac{1}{2} + \frac{1}{3} = \frac{11}{6}$

$\implies {R}_{T} = \frac{6}{11} \Omega$