Question

(10%) Problem 7: Suppose a large power plant generates electricity at 12.0 kV. Its old transformer once converted this voltage to 345 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 Vi = 345 kV V2 - 760 kV 50% Part (a) If the overall power output is 1000.0 MW and line resistance is 2.00 2. what was the power loss, in watts, in the old power lines which left the plant? & 50% Part (b) If the overall power output is 1000.0 MW and line resistance is 2.00 , what is the power loss, in watts, in the new power lines which leave the plant? Grade Summary Ploss, 2- Deductions 096 Potential 10096 sino cos t ano ( 7 8 Submissions Attempts remaining: 10 cotan() asin( acoso E 4 5 6 (0% per attempt) atan acotan s inh) 1 2 3 detailed view cosho tanhocolanh OL 7:55 AM

Answer 1

Part(a):-Output power with old transformer-

  $\mathbf{P=1000MW=1000\times 10^6W=10^9W}$

Output voltage-

$\mathbf{V_{out}=345KV=345\times 10^3V=3.45\times 10^5V}$

Output power-

$\mathbf{P=V_{out}I_{out}}$

$\mathbf{\Rightarrow I_{out}=\frac{P}{V_{out}}}$

$\mathbf{\Rightarrow I_{out}=\frac{10^9}{3.45\times 10^5}}$

$\mathbf{\Rightarrow I_{out}=2.899\times 10^3A}$

Power loss in lines-

$\mathbf{P_{loss}=I_{out}^2R}$

$\mathbf{\Rightarrow P_{loss}={(2.899\times 10^3)}^2\times 2}$

$\mathbf{\Rightarrow P_{loss}=1.68\times 10^7W}$

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Part(b)-In this case-

$\mathbf{I_{out}=\frac{P}{V_{out}}}$

$\mathbf{I_{out}=\frac{10^9}{760\times 10^3}}$

$\mathbf{I_{out}=1.316\times 10^3W}$

power loss in lines-

$\mathbf{P=I_{out}^2R}$

$\mathbf{P=(1.316\times 10^3)^2\times 2}$

$\mathbf{P_{loss,2}=3.46\times 10^6W=3.46MW}$