Question

How much power is produced if a voltage of `9 V` is applied to a circuit with a resistance of `3 Omega`?

Answer 1

I found: `27"Watts"`

Explanation:

Consider that your voltage is telling you the quantity of energy, in joules, carried by each Couomb of charge; in our case every coulomb of charge is carring `9` Joules of energy. But how many coulomb are passing by to give you the energy in, say, `1` second?
Ohm tells us that in our wire of resistence `3Omega` passes a current given as:
`i=V/R=9/3=3A` but this current tells us that we have `3` Coulombs each second passing by!!!

So we can join volts and amperes together to say that the power `P` (equal to energy/time) will be:

`P=Vi="joule"/"Coulomb"*"Coulomb"/"time"="Joule"/"time"="Watts"`
YES!!!

so:

Power`=3*9=27"Watts"`

Answer 2

`=27W`

Explanation:

Power P=`V^2/R` , where V = voltage and R = resistance
`:.P=V^2/R=9^2/3=27W`