Anonymous
Anonymous asked in Science & MathematicsEngineering · 5 months ago

# A power station delivers 455kW of power at a voltage of 4.00 x 10^4V through lines with a resistance of 5ohms. ?

A power station delivers 455kW of power at an input voltage of 4.00 x 10^4V to a factory through lines whose total resistance is 5.00ohms. If the same power was required, but the input voltage was reduced to 1.00 x 10^4V, by what factor would the power wasted in the lines be multiplied?

I'm struggling with this problem, and I would really appreciate any help with it.

The given answer is 16 Times

Thank you!

Relevance
• We know  Power = V*I.  If V1 = V/4 then I1 = 4*I.  Losses  = I²*5Ω = (4*I)²*5Ω = 16*I*5Ω

Hope that helps.

• Anonymous
5 months ago

Assuming this is all single phase (not realistic but likely the basis), P loss = R * I^2

If the resistance is fixed and you reduced the voltage to 1/4 of the original voltage, the current must increase by a factor of 4.  Since the resistance is fixed, 4x the current = 4^2 or 16x the internal power losses.

• First of all, I would say that writing "4.00 x 10^4V" is odd. It's much more understandable to write 40,000 V.

Secondly, I would figure the current and voltage at the factory.