Parallel resistance in electric circuits Introduction:

Two resistors, R1 and R2,  in parallel (denoted R1 || R2) have a combined resistance Rp given as:

$$R_{P_2} = \frac{R_1\cdot R_2}{R_1+R_2}$$
or as suggested in comments:

$$R_{P_2} = \frac{1}{\frac{1}{R_1} + \frac{1}{R_2}}$$

Three resistors, R1, R2 and R3 in parallel (R1 || R2 || R3) have a combined resistance (R1 || R2) || R3 = Rp || R3 :

$$R_{P_3} = \frac{\frac{R_1\cdot R_2}{R_1+R_2}\cdot R_3}{\frac{R_1\cdot R_2}{R_1+R_2}+R_3}$$

or, again as suggested in comments:

$$R_{P_3} = \frac{1}{\frac{1}{R_1} + \frac{1}{R_2}+ \frac{1}{R_3}}$$

These formulas can of course be extended to an indefinite number of resistors.



Challenge:

Take a list of positive resistor values as input, and output the combined resistance if they were placed in parallel in an electric circuit. You may not assume a maximum number of resistors (except that your computer can handle it of course).

Test cases:

1, 1
0.5

1, 1, 1
0.3333333

4, 6, 3
1.3333333

20, 14, 18, 8, 2, 12
1.1295

10, 10, 20, 30, 40, 50, 60, 70, 80, 90
2.6117  




Shortest code in each language wins. Explanations are highly encouraged.
05AB1E, 5 3 bytes
zOz

Try it online!

Explanation
z                     # compute 1/x for each x in input 
 O                    # sum input 
  z                   # compute 1/sum