A large power plant generates electricity at 12.0 kV. Its old transformer once c

Question

A large power plant generates electricity at 12.0 kV. Its old transformer once converted the voltage to 381 kV. The secondary of this transformer is being replaced so that its output can be 476 kV for more efficient cross-country transmission on upgraded transmission lines.

(a) What is the ratio of turns in the new secondary to turns in the old secondary?

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(b) What is the ratio of new current output to old output (at 381 kV) for the same power?

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(c) If the upgraded transmission lines have the same resistance, what is the ratio of new line power loss to old?

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Explanation / Answer

Part (a)

The ratio of turns in old transformer is,

       Es1 / Ep = Ns1 / Np

Where Es1, Ep are voltage in secondary and primary, Ns1, Np are number of turns in secondary and primary.

The ratio of turns in new transformer is,

       Es2 / Ep = Ns2 / Np

The ratio of above two equations gives the ratio of turns in the new secondary to turns in the old secondary.

       Ns2 / Ns1 = Es2 / Es1 = 476 kv / 381 kv = 1.25            (ANSWER)

Part (b)

The ratio of turns in old transformer is,

       Es1 / Ep = Ip / Is1

Where Is1, Ip are current in secondary and primary.

The ratio of turns in new transformer is,

       Es2 / Ep = Ip / Is2

The ratio of above two equations gives the ratio of turns in the new secondary to turns in the old secondary.

       Is2 / Is1 = Es1 / Es2 = 381 kv /476 kv = 0.8               (ANSWER)

Part (c)

The power is equal to product of square of current and resistance.

The power loss ratio at constant resistance is,

Pnew / Pold = Is2 ^ 2 / Is1 ^2 = (0.8 ) ^2 =0.64                (ANSWER)

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