Question

What is the parallel equivalent of two 1000 W resistors in parallel?

Answer 1

I think you mean `Omega` and not `W`. The answer is `500Omega`. If you actually mean `W`, the question should be resistors consuming `1000` `W`. BTW, resistors don't normally consume `1000` `W`. We call resistors that consume `1000` `W` a heater.

Resistors in parallel use the formula:

`1/(R_T)=1/(R_1)+1/(R_2)`
`1/(R_T)=1/(1000)+1/(1000)`
`1/(R_T)=2/(1000)=1/(500)`
`R_T=500Omega`

If you actually mean `W`, then we need a different calculation:

`P=VI=VV/R=(V^2)/R`
`1000=(V^2)/R`
This is for 1 resistor.

Recall that the voltage is the same across the resistors in parallel, so `V_T=V`. So, summing up the wattage, we get:
`2000=((V_T)^2)/(R_T)=(V^2)/(R_T)`
`2(V^2)/R=(V^2)/(R_T)`
`R_T=1/2R`

Since we are not provided with any voltage or resistance, we simply have to leave the answer as `R_T=1/2R`, where `R` is the resistance of 1 resistor. This is the same relation as calculating 2 - `1000Omega` resistors in parallel.