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

1 Answer
Amory W.
Aug 24, 2014

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.

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