2.0 MW is to arrive at a large shopping mall over two 0.100Ω lines. Estimate how much power is saved if 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.

55 MW.

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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