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Electricity question (Physics A Level)

Hi I was wondering if someone could help me with the following question:
A power of 100kW at a potential difference of 10kV is transmitted to a load resistor through cables of total resistance 5ohms. What is the power loss in the cables?


The two equations for power that I know are I^2R and V^2/R. However, using the former with I given by 100kW/10kV and subbing this into equation above gives 500W (which is correct) but by subbing V as 10kV into above equation it gives 20MW which is not correct.
I was wondering why these two equations give different values? Thanks for the help!
Reply 1
When they talk about power loss in cables, its due to the build up of eddy current. It’s like how on the national Grid they step-down the current to keep the system highly efficient.


Original post by Felix'sfreckles
Hi I was wondering if someone could help me with the following question:
A power of 100kW at a potential difference of 10kV is transmitted to a load resistor through cables of total resistance 5ohms. What is the power loss in the cables?


The two equations for power that I know are I^2R and V^2/R. However, using the former with I given by 100kW/10kV and subbing this into equation above gives 500W (which is correct) but by subbing V as 10kV into above equation it gives 20MW which is not correct.
I was wondering why these two equations give different values? Thanks for the help!
Reply 2
I interpret the setup of the question as meaning the load resistor has 10kV across it and it is dissipating 100kW

from that you can calculate the current is 10A in the load resistor and because the load resistor is in series with the transmission lines the current in the resistance of transmission lines must also be 10A

so here you can do I2 R to get 500W because the current in the 5 Ohm resistance is 10A

but it's incorrect to do V2 / R to get 20MW because you're using the voltage across the load resistor and the resistance of the transmission line.

if you needed to use V2/R you'd need an additional step to calculate the voltage across the 5 ohm resistance of the transmission lines.

you could do V=IR to find the voltage across the resistance of the transmission lines is 50V

then using that 50V in V2/R you'd get the correct answer for the power dissipation in the lines

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