Misconceptions in Calculating Power Dissipation in Electrical Circuits

[Gunman]

Homework Statement

A 100 kW generator supplies power at a p.d of 10kV through cables of total resistance 5 Ohms. Calculate the supply current and the power dissipated in the cables.

Homework Equations

P = IV
V=IR
Q=It

The Attempt at a Solution

Supply current:
P=IV
100 kW = (I)(10kV)
I=10A
Supply current 10 A.

But I get different answers when I try to find the power dissipated in the cable.
By using this formulae , P = (V*V)/R I get a huge number which is wrong because it is more than the power generated but when I use P = ( I * I ) / R , I get the correct answer.

Think I have a misconception about this [ P = (V*V)/R ] . Can someone tell me where I am wrong? and why so? Thanks in advance. =)

 

[cryptoguy]

The power equation is P = I*I*R (sub in ohm's law into the power equation)

 

[blochwave]

Yah I think he typo'd there. What he's missing is that power generator is FORCING a certain power output, and thus FORCING a certain current through that potential difference, which you found correctly

However if that power generator wasn't limiting you, you would have 10kV across 5 ohms, which corresponds to a current flowing of 2000amps, which when put into P=IV, doing 2000*10kV gives you the incorrect huge answer you got

by using P=V^2/R you're finding the power dissipated in 5ohm wires with a potential difference of 10kV, ignoring the fact that you're limited to 100kW from the power generator. By finding the actual current through the wires, you incorporate that

 

[Gunman]

Ohh.Thanks blochwave! Understood why I was wrong. =)