Why doesn't V = IR? PHYA4. Transformers.

P loss is given by I²R.

But the reason I am confused is, that's the equation for power generally.

A power station delivers 530 kW of power at 12,000V to a factory through wires with total resistance 2.5. How much power is wasted?

IV = 530,000.
I = 530,000 / 12,000 = 41.166...A.

But, V = IR = 41.166... * 2.5 = 110.4166...V.

Why? P = VI = I²R.

How do you know which one is power loss and which one is total power?

Thanks.

Reply 1

uberteknik

Original post by Sayonara

They are all related.

V = IR

P = VI

so substituting the first expression for V in the second gives:

P = (IR)*I = I²R

Similarly

I = V/R

P = VI

Substituting I into the second expression gives:

P = (V/R)*V = V²/R

Plug in the values and all three will produce the same answer. Try it.

In your answer, you calculated the voltage dropped across the line resistance of 2.5 ohms.

i.e. 110.417V was dropped across the cable not the load.

So the power dissipated in that line resistance is

V²/R = (110.417)²/2.5 = 4877 watts.

Using the other equation:

power dissipated = I²R = 44.166²*2.5 = 4877 watts

or

power = VI = 110.417*44.166 = 4877 watts

You can use any of the equations, just remember that VI is normally used to find the total power the transformer can handle safely (VA rating) or the total d.c. power available from a source.