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Suppose a large power plant generates electricity at 12.0 kV. Its old transformer once converted this voltage to 365 kV. The secondary coil of this transformer is being replaced so that its output can be 760 kV for more efficient cross-country transmission on upgraded transmission lines. Randomized Variables V1

Part (a) What is the ratio of turns in the new secondary to the number of turns in the old secondary? 33% Part (b) What is the ratio of new current output to the old current output for the same power input to the transformer?

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boffeemadrid

Answer:

[tex]\dfrac{N_s}{N_p}=2.08219[/tex]

[tex]\dfrac{I_{sn}}{I_{so}}=0.48289[/tex]

Explanation:

V denotes voltage

I denotes current

p denotes primary

s denotes secondary

o denotes old

n denotes new

N denotes number of turns

For transformers we have the following relation

[tex]\dfrac{V_s}{V_p}=\dfrac{N_s}{N_p}\\\Rightarrow \dfrac{N_s}{N_p}=\dfrac{760}{365}\\\Rightarrow \dfrac{N_s}{N_p}=2.08219[/tex]

The required ratio is [tex]\dfrac{N_s}{N_p}=2.08219[/tex]

For current

[tex]\dfrac{I_{so}}{I_{sn}}=\dfrac{V_{sn}}{V_{sn}}\\\Rightarrow \dfrac{I_{sn}}{I_{so}}=\dfrac{367}{760}\\\Rightarrow \dfrac{I_{sn}}{I_{so}}=0.48289[/tex]

The required ratio is [tex]\dfrac{I_{sn}}{I_{so}}=0.48289[/tex]

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