Question

You connect three resistors with resistances r, 2r, and 3r in parallel. The equivalent resistance of the three resistors will have a value that is?

1) r/6
2) r/3
3) r/2
4) r

Answer 1

The equivalent resistance of three resistors with resistances r, 2r, and 3r connected in parallel is 6r/11, which is less than r and approximately r/3 when rounding to the nearest option provided.

Step-by-step explanation:

When you connect three resistors with resistances r, 2r, and 3r in parallel, the total (equivalent) resistance can be found using the formula for parallel resistors:

1/Requiv = 1/r + 1/(2r) + 1/(3r)

Simplifying this equation, we get:

1/Requiv = (1 + 1/2 + 1/3)/r = (6/6 + 3/6 + 2/6)/r = (11/6)/r

Therefore, Requiv = 6r/11. Because 6r/11 is always less than r, the equivalent resistance of the three resistors when connected in parallel will be less than the resistance of the smallest individual resistor. The value of Requiv is not exactly one of the options given in the initial question; however, it is closest to option 2) r/3 if we were to round to the nearest option provided.