Answer:
55 MW.
Step-by-step explanation:
So, we are given the following data or parameters Below;
=> "2.0 MW is to arrive at a large shopping mall over two 0.100Ω line.
=> " the voltage is stepped up from 120 V to 1200 V and then down again, rather than simply transmitting at 120 V."
=> "Assume the transformers are each 99% efficient."
STEP ONE: determine the current in the transmission line.
Output Current, i = Power/ voltage.
Output Current,i = (2.0 MW × 10^6 W/ 1 MW)/120.
Output Current,i = 1.66 × 10^4 A.
Therefore, current in the transmission line = output voltage × output current/99% × line voltage.
= 120 × 1.66 × 10^4/ 99% × 1200 = 1.68 × 10^3 A.
STEP TWO: determine the power loss in the two lines.
Power loss = i^2 × Resistance
Power loss = (1.66 × 10^4 )^2 × 0.1 × 2 = 5.5 × 10^7 watt.
STEP THREE: determine the power generated.
Power generated = 2 × 10^6 +5.5 × 10^7.
Power generated = 5.57 × 10^7 watt.
STEP FOUR: determine the step down transformer power.
= 2 × 10^6/99% = 2.02 × 10^6.
Thus, 2.02 × 10^6 + 5.57 × 10^5 = 2.58 × 10^6 watt.
STEP FIVE: Determine the total power and the saved power.
Total power = 2.58 × 10^6/ 99%= 2.6 × 10^6.
Saved power = 5.7 × 10^7 - 2.6 × 10^6 .
Conversion to MW gives saved power = 55 MW.
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