CATAGORY: Electricity & Magnetism
QUESTION:   In my exam paper, the question asked "Why is less energy loss
in overhead cable when a hiher voltage is used?" I didn't answer it, the
answer was because a higher voltage means lower current, and so less heat
is dissipated.
  But I thought Ohm's law stated that voltage is proportional to
current!!!!! And also, I=v/R.  If R is constant how can I be lower when V
is higher??????

Back to subcatalog.

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OK here is the answer!  The trick is to realize that the overhead power
line MUST DELIVER a certain amount of power to its customers.

(1)      Power delivered = current x voltage

                         or

                   P(del.) = I V

>From this we can solve for I

(2)                        P(del.)
                      I  = -------
                              V

Note: The delivered power, P(del.), is (not the same as the lost power!)
      fixes the value of the current.

The power lost in the line is then given by the square of the current
times the resistance of the line.


(3)                 P(lost) = I^2 R

Substitution of (2) into (3) gives

(4)                        [P(del.)]^2
                 P(lost) = -----------  R
                             [V]^2


Note that P(lost) is proportional to the inverse square of V so the higher
the voltage the smaller the P(lost).  I think you were confusing the
delivered power with the lost power.