(II) An electric power plant can produce electricity at a fixedpower P, but the

Question

(II) An electric power plant can produce electricity at a fixedpower P, but the plant operator is free to choose the voltage V atwhich it is produced. This electricity is carried as anelectric current I through a transmission line (resistance R) fromthe plant to the user, where it provides the user with electricpower P'. (a) Show that the reduction in power P = P - P' dueto transmission losses given by P =P2R/V2. (b) In order to reduce power lossesduring transmission, should the operator choose V to be as large oras small as possible?

Explanation / Answer

  a.    Powerlost   =   I2 * R    I   =   Currentthrough transmissionline,   R   =   Totalresistacnce of transmission lines    Also   Current   I   =   P/ V    =>   P   =   (P/V)2* R   =   P2 * R /V2    b.   Since V ( voltage atwhich transmission is done) appears in denominator ( i.e. powerloss is inversely proportional to square of voltage), power losscould be minimised by keeping voltage as high as possible.    b.   Since V ( voltage atwhich transmission is done) appears in denominator ( i.e. powerloss is inversely proportional to square of voltage), power losscould be minimised by keeping voltage as high as possible.

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