How to calculate power loss in transmission cables?

[svar]

Power station generates 120kW

Electricity can be transmitted either at 240V or at 24000V using a step-up transformer.

The cables have total resistance of 0.4W

What is the power loss when voltage is transmitted at:

1) 240V
2) 24000V



I AM SURE YOU CAN WORK THIS OUT USING I squared R (or as I have typed it: I^2R)

Using 240V:
P = IV, therefore I = 500A
P = I^2R = 100000W

Using 24000V:
P = IV, 120000W = I24000V, therefore I = 5A
P = I^2R = 10A

Less power loss when using higher voltage




My question begins with the premises called Ohm’s law and Joules’ law which lead to the textbook equations I^2R = V^2/R = P

Power loss using I^2R works out different to power loss using V^2/R, given all textbooks equate I^2R with V^2/R

THIS FAILS TO WORK WITH ABOVE QUESTION!

Infact P=V^/R indicates greater power loss at higher voltages (for same resistance), negating the idea of stepping up voltages to reduce power loss in electrical transmission. In your solution please using the values I have used above in the question (taken from a textbook)

Please clarify - at a level for 16-18 year old physics students. Thanks.

 

[berkeman]

The thing that is confusing you is the definition of V.

The V in V^2/R is the voltage drop across the wire, not the full voltage being transmitted. The voltage drop across the wire is V=IR, which will be much smaller than the transmitted voltage. Make sense?

BTW, you have a typo in your question where you say the resistance is 0.4W. You meant 0.4 Ohms most likely.

Welcome to the PF.

 

[Alevelphysics]

If

P = power generated at power station
V = voltage at which power is transmitted
R = Resisitance of transmission cable

then

Current in the transmission cables = P/V

*Power loss is not equal to V^2/R because this V does not represent potential drop across the cables.

If the cables are connected to your home then Power = V^2 / (Resistance of cables + Resistance of your house)

Hence Power loss at the cables = I^2 R or (P/V)^2 R

 

[psychophysics]

-------------------------------------------
P = IV = I^2R = V^2/R
-------------------------------------------
Power loss through transmission cable is (I^2R)
-------------------------------------------

Exampleower station produce 500MW
-Step up transformer is used to step up the voltage to 250KW
-Cable has resistance of 10ohms

P=VI
500x10^6=250x10^3(I)

I=500x10^6/250x10^3

I=2000A

Power loss is = I^2R
Power loss is = 2000^2 x 10
Power loss is = 4x10^7W

Ratio: power loss/ original
Ratio: 400x10^5/500x10^6 = 0.08 = 8% power loss

 

[Greg Bernhardt]

The power dissipation (P diss ) in a transmission cable is basically the measured loss (P meas ) multiplied with the cable's voltage (V c ) and current (I c ) P diss = P meas x V c x I c How to calculate cable loss per 100 m (328 ft)? To calculate cable loss per 100 m (328 ft) we need the cable's ohmic loss (P ohm ) and the cable's cross-sectional area (A c ) P loss per 100 m = P ohm x A c Since the cross-sectional area stays the same, the loss per length will stay the same, independent of the cable's length.