Electric Power: V^2/ohm Has SI Units of Power

[predentalgirl1]

Show the quantity volts squared per ohm (V^2/ohm) has SI units of power.








P = V x I
where
P is the power (watt or W)
V is the potential difference (volt or V)
I is the current (ampere or A)
From Ohm’s law
I = V / R
where
R is the resistance (Ohm or Ω).
So substituting in the above equation
P = V x (V/R)
P = V2 /R
So in unit , watt = (volt)2 / Ω


OR
I can rewrite, V^2/R = V.V/R = V.I
From definition of potential difference as Work done per unit charge, V = W/q
Unit volt, V = unit of W/unitof chaarge = J/C
Also current = charge/time
I = C/s
so, V^2/R = V.V/R = V.I
= J/C xC/s = J/s
= watt, (unit of power.)


Which seems most reasonable?

 

[rock.freak667]

You should use the 2nd one as that uses what they gave you V^2/omega to get J/s.

 

[Moetasim]

Both are reasonable and correct ways to show that V^2/ohm has SI units of power. The first method uses Ohm's law and the definition of power, while the second method uses the definitions of potential difference and current. Both methods show that V^2/ohm is equivalent to watts, the SI unit of power.