Question

Определите кпд ЛЭП, если её длина 30 км, сечение медного провода, из которого она выполнена равна 16 мм^2. Сила тока равна 12 А, напряжение 630 В(p=1,72•10^-2 Ом•мм^2/м)

Answer 1

Η=Pполезное/Pзатраченное;
Pполезное=Pзатраченное-Pпотерь;
η=(Pзатраченное-Pпотерь)/Pзатраченное;
Pпотерь=I²·Rлинии; Pзатраченное=UI; Rлинии=ρl/S;
η=(UI-I²·ρl/s)/UI; η=(630·12-12²·1.72·10⁻²·30000/16)/(630·12)≈0.39≈39%
Ответ: η≈39%

Answer 2

Calculating the Efficiency of the Power Line

To calculate the efficiency of the power line, we can use the formula:

Efficiency (η) = (Output Power / Input Power) × 100%

Where: - Output Power = Voltage × Current - Input Power = Voltage × Current + I^2R losses

Given: - Length of the power line (L) = 30 km - Cross-sectional area of the copper wire (A) = 16 mm^2 - Current (I) = 12 A - Voltage (V) = 630 V - Specific resistance of the copper wire (p) = 1.72 × 10^-2 Ω·mm^2/m

Calculating the Resistance of the Copper Wire

First, we need to calculate the resistance of the copper wire using the formula:

Resistance (R) = (Specific resistance × Length) / Cross-sectional area

Plugging in the values: R = (1.72 × 10^-2 Ω·mm^2/m × 30,000 m) / 16 mm^2

Calculating the resistance: R = (1.72 × 10^-2 × 30,000) / 16 = 32.25 Ω

Calculating the Input Power

Next, we can calculate the input power using the formula:

Input Power = Voltage × Current + I^2R

Plugging in the values: Input Power = 630 V × 12 A + (12 A)^2 × 32.25 Ω

Calculating the input power: Input Power = 7560 W + 4644 W = 12204 W

Calculating the Output Power

Now, we can calculate the output power using the formula:

Output Power = Voltage × Current

Plugging in the values: Output Power = 630 V × 12 A

Calculating the output power: Output Power = 7560 W

Calculating the Efficiency

Finally, we can calculate the efficiency using the formula:

Efficiency (η) = (Output Power / Input Power) × 100%

Plugging in the values: Efficiency (η) = (7560 W / 12204 W) × 100%

Calculating the efficiency: Efficiency (η) = 61.96%

Therefore, the efficiency of the power line is approximately 61.96%.