Misconceptions in Calculating Power Dissipation in Electrical Circuits

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SUMMARY

The discussion centers on calculating power dissipation in electrical circuits, specifically using a 100 kW generator supplying power at 10 kV through cables with a total resistance of 5 Ohms. The correct supply current is determined to be 10 A using the formula P = IV. A misconception arises when attempting to calculate power dissipation using P = (V^2)/R, which yields incorrect results due to ignoring the generator's power limitation. The accurate formula for power dissipation in this scenario is P = I^2 * R, which incorporates the actual current flowing through the circuit.

PREREQUISITES
  • Understanding of Ohm's Law (V = IR)
  • Familiarity with power equations (P = IV, P = I^2R)
  • Knowledge of electrical circuit components (generators, resistors)
  • Basic grasp of power dissipation concepts in electrical engineering
NEXT STEPS
  • Study the implications of power limitations in electrical circuits
  • Learn about the relationship between voltage, current, and resistance in circuit analysis
  • Explore advanced power calculation techniques in AC and DC circuits
  • Investigate the effects of resistance on power loss in electrical systems
USEFUL FOR

Electrical engineering students, circuit designers, and professionals involved in power generation and distribution who seek to deepen their understanding of power dissipation in electrical circuits.

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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. =)
 
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The power equation is P = I*I*R (sub in ohm's law into the power equation)
 
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
 
Ohh.Thanks blochwave! Understood why I was wrong. =)
 

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