Final answer:
To transmit 100 MW of power at 200 kV, a current of 500 A is needed. The power dissipated by transmission lines with a resistance of 1.00 Ω is 250 kW, which is 0.25% of the total power transmitted.
Step-by-step explanation:
To answer the question regarding the transmission of power, we use the formula Power (P) = Voltage (V) * Current (I). To find the current required to transmit 100 MW (1.00×10² MW) of power at 200 kV
- Current (I) = Power (P) / Voltage (V)
- Current (I) = 1.00×10² MW / 200 kV
- Current (I) = 500 A
For the second part, the power dissipated by the transmission lines with a resistance of 1.00 Ω can be found using the formula Power Dissipated (Pd) = Current^2 (I²) * Resistance (R):
- Power Dissipated (Pd) = (500 A)² * 1.00 Ω
- Power Dissipated (Pd) = 250,000 W or 250 kW
Finally, to calculate the percentage of power lost in the transmission lines:
- Percentage Loss = (Power Dissipated / Power Transmitted) * 100
- Percentage Loss = (250 kW / 100,000 kW) * 100
- Percentage Loss = 0.25%