Given that the effective resistance is 2 OHM, how much is worth the resistance of each one of these OHMS resistors.

Question

Three equal Resistors are put up in a way in where two are related between themselves and at the same time in parallel with the third resistor. Given that the effective resistance is 2 OHM, how much is worth the resistance of each one of these OHMS resistors.

A) 100 OHM

B) 30 OHM

C) 1 OHM

D) 10 OHM

E) 3 OHM

Answer 1

E) 3ohms

It is best to begin with a picture of these 3 resistors; however, it is also possible to complete this problem without drawing. Resistance is best figured out by working backwards, so we should start by creating an equation for the resistance in parallel.

1/Req= 1/R₁ + 1/R₂

In this case, R₁ will be the combination of the resistors in series, so our equation will look more like:

1/ R_eq= 1/ (R₁+R₂) +1/R₂

Since all three resistors are equal, we can substitute all of the R's for x to make:

1/Req= 1/(x+x) +1/x

Plugging in the equivalent resistance of 2, we get:

1/2=1/2x +1/x

Now we just have to solve algebraically for x!

*multiply both sides by x; then multiply by 2

x=3