A large power plant generates electricity at 12.0 kV. Its old transformer once converted the voltage to 425 kV. The secondary of this transformer is being replaced so that its output can be 510 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?

(b) What is the ratio of new current output to old output (at 425 kV) for the same power?

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

a) 1.2

b) 0.833

c) 0.694

Explanation:

a) The transformer steps up the voltage from 12000 V to 425000 V. Voltage in primary is 12000 V and in the secondary it is 425000 V in old transformer

If n₁ be no of turns in primary coil and n₂ be no of turns in secondary coils

the formula is

n₂ / n₁ = voltage in secondary / voltage in primary

n₂ / n₁ = 425000 / 12000

ratio of turns in old transformer

= 35.42

ratio of turns in new transformer

n₃ / n₁ = 510 / 12 (n₃ is no of turns in the secondary of new transformer)

= 42.5

T he ratio of turns in the new secondary compared with the old secondary

n₃ / n₂ = 42.5 / 35.42

= 1.2

b) Current in secondary / current in primary

= turns in primary / turns in secondary

current output ratio of old

= Current in secondary / current in primary

= n₁ / n₂

= 12 / 425

=.0282

current output ratio of new

= Current in secondary / current in primary

= n₁ / n₃

= 12 / 510

=.0235

The ratio of new current output to old output (at 425 kV) for the same power

=.0235 /.0282

=.833

c) power loss in new

= (current in secondary) ² x resistance of secondary

= (.0235 x current in primary) ² x R

= 5.52 X 10⁻⁴ X (current in primary) ² x R

power loss in old

= (current in secondary) ² x resistance of secondary

= (.0282 x current in primary) ² x R

= 7.95 X 10⁻⁴ X (current in primary) ² x R

ratio of new line power loss to old

= 5.52 / 7.95

=.694