Which one will have more losses. AC line carrying 400 kv for 40 km or DC line carrying 400 kv for 40 km?



Answer:
AC line carrying 400 kv for 40 km
The DC line will have a much greater power loss than the AC line.

Power losses as head are given by Current^2 x Resistance. The DC line would heat up much more causing increased resistance.

All bulk power transmission lines in the world use AC transmission - surely they wouldn't use this method if it were 'less efficient' than DC transmission.

If you are talking about HVDC transmission, this is a completely different issue.
http://en.wikipedia.org/wiki/hvdc...
There will be equal loss in both the cases becuase 400 Kv is the vitual power in case of ac and it is the effective dc value of the ac power.
The difference will be small, but the AC line will have greater losses because:

(1) The peak voltage on a 400kV AC line is greater than 400kV, so losses causes by insulation leakage will be greater

(2) There will be some losses due to radiation and to hysteresis in surrounding magnetic and dielectric materials simply because it is AC, not DC

BUT

With DC it would be very hard to get up to 400kV in the first place, and as resistance losses (the really important bit) vary inversely with the square of the voltage it's much better to use high voltage AC than lower voltage DC – that's why everyone does it.
The AC will be more lossy. A 40 km transmission line is inductive. As frequency increases the greater the impedance this line will present and as such will be more lossy. We use AC because it is more managable (you cant use transformers with DC)
AC line have more loses and hence the technology HVDC. High Voltage DC transmission systems in many developed countries.
In India also there are only a few HVDC lines but majority are AC transmission lines and hence rate of power loss is high.

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