Electrical Power Transmission Losses?
Could someone please explain where my confusion is arising? This is how I see it now:
I'll be using four equations:
P=IV
P=(I^2)R
P=V^2/R
V=IZ (load impedance plus line resistance)
Lets start with assigning initial values for V, I, and Z according to ohm's law:
V = 10 volts
I = 10 amps
Z = 1 ohm
R = line resistance (included in Z) = 0.5 ohm
So power being delivered is P = IV = (10)(10) = 100 watts
This is where I am confused:
The power loss in line is given by P =(I^2)R, as well as by P = V^2/R. These two equations contradict each other:
P = (I^2)R = (100)(0.5) = 50 watts
P = V^2/R = (100)/(0.5) = 200 watts
I know something I’ve done here is wrong. What is it?
More Questions From This User See All
Answers & Comments
Verified answer
In the last equation you have listed:
P = V^2/R = (100)/(0.5) = 200 watts
....the "V" shouldn't be 10 volts and so V² doesn't equal 100.
The voltage applied to the load is 10 volts, but since the load is 1 ohm, 0.5 ohm of which is line resistance, there are effectively two 0.5 ohm resistances in series and the 10 volts is divided equally between these resistances.
So the voltage drop on the 0.5 ohm line resistance is 5 volts.
So P = V²/R = (25)/(0.5) = 50 watts