Register to reply

How to calculate power loss in transmission cables?

Share this thread:
Sep23-08, 10:28 AM
P: 6
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 Ohmís law and Joulesí 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 text books equate I^2R with V^2/R


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 text book)

Please clarify - at a level for 16-18 year old physics students. Thanks.
Phys.Org News Partner Science news on
What lit up the universe?
Sheepdogs use just two simple rules to round up large herds of sheep
Animals first flex their muscles
Sep23-08, 11:14 AM
berkeman's Avatar
P: 41,041
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.
Oct27-09, 03:55 AM
P: 1

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


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

Aug15-11, 02:42 AM
P: 1
How to calculate power loss in transmission cables?

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

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




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

Register to reply

Related Discussions
Fluids: calculate pressure loss due to turns in pipe flow Mechanical Engineering 9
How to calculate heat loss Materials & Chemical Engineering 0
How to Calculate Transmission Spetrum Atomic, Solid State, Comp. Physics 3
Power loss in transmission lines (Electromagnetic Induction and Faraday's Law) Introductory Physics Homework 1
Power cables info Computing & Technology 10