Question

A circuit has 3 resistors, all connected in parallel. Let R1 = 4.0 Ω, R2 = 3.0 Ω, and R3 = 6.0 Ω. What is the equivalent resistance of the circuit? Show all work and include units of measure.

Answer 1

`1.33\Omega`

Step-by-step explanation:

The equivalent resistance of three resistors connected in parallel is given by:

`(1)/(R_T) = (1)/(R_1)+(1)/(R_2)+(1)/(R_3)`

where in this problem we have

`R_1 = 4.0\Omega`

`R_2 = 3.0 \Omega`

`R_3 = 6.0 \Omega`

Substituting into the equation, we find

`(1)/(R_T) = (1)/(4.0\Omega)+(1)/(3.0\Omega)+(1)/(6.0\Omega)=0.75\Omega^(-1)`

And so, the equivalent resistance is

`R_T=(1)/(0.75 \Omega^(-1))=1.33\Omega`