Question

Передача электроэнергии мощностью 650 кВт от электростанции к потребителям производится по линии электропередач длиной 200 км. Доля мощности, теряемой на нагрев алюминиевых проводов, составляет 8 % от передаваемой мощности. Площадь поперечного сечения провода равна 11 мм². Определи напряжение, при котором производится электропередача.

Answer 1

Ответ:

Объяснение:

Дано:

P = 650 кВт

l = 200 км = 2*10^5 м

Pпотери = P*0.08

Sсечения = 11 мм^2

ρ ( удельное сопротивление алюминия ) =

= 28*10^-3 (Ом*мм^2)/м

Найти: U - ?

Найдем мощность при которой будет производится электропередача с потерями:

Pпотери = 650 * 0.08 = 52 кВт, тогда P = 650-52 = 598 кВт.

$P=\frac{U^{2} }{R}$

Найдем R:

R=ρl/S=(2*10^5*28*10^-3)/11 = 509 Ом.

Находим напряжение:

$U^{2}=P*R$= 509*598*10^3=3*10^8 В

U = 17320,5 В.

Answer 2

Calculation of Voltage for Power Transmission

To determine the voltage at which the power transmission is carried out, we can use the information provided.

Given: - Power (P) = 650 kW - Length of transmission line (L) = 200 km - Power loss due to heating of aluminum conductors = 8% of transmitted power - Cross-sectional area of the conductor (A) = 11 mm²

To calculate the voltage, we can use the formula:

Power (P) = Voltage (V) × Current (I)

We can rearrange the formula to solve for voltage:

Voltage (V) = Power (P) / Current (I)

To find the current, we need to calculate the power loss due to heating of the aluminum conductors.

The power loss due to heating can be calculated using the formula:

Power Loss = (Resistance × Current²) × Length

The resistance of the conductor can be calculated using the formula:

Resistance = Resistivity × Length / Cross-sectional area

The resistivity of aluminum is approximately 2.65 × 10^-8 Ω·m.

Let's calculate the voltage step by step:

1. Calculate the resistance of the conductor: - Resistivity (ρ) = 2.65 × 10^-8 Ω·m - Length (L) = 200 km = 200,000 m - Cross-sectional area (A) = 11 mm² = 11 × 10^-6 m²

Resistance (R) = Resistivity (ρ) × Length (L) / Cross-sectional area (A)

2. Calculate the power loss due to heating: - Power (P) = 650 kW - Power loss (PL) = 8% of transmitted power

Power loss (PL) = Power (P) × Power loss (%) / 100

3. Calculate the current: - Power loss (PL) = (Resistance (R) × Current (I)²) × Length (L)

Current (I) = sqrt(Power loss (PL) / (Resistance (R) × Length (L)))

4. Calculate the voltage: - Voltage (V) = Power (P) / Current (I)

Let's calculate the voltage using the given values:

1. Calculate the resistance of the conductor: Resistance (R) = (2.65 × 10^-8 Ω·m) × (200,000 m) / (11 × 10^-6 m²)

2. Calculate the power loss due to heating: Power loss (PL) = (650 kW) × (8%) / 100

3. Calculate the current: Current (I) = sqrt((Power loss (PL)) / ((Resistance (R)) × (Length (L))))

4. Calculate the voltage: Voltage (V) = (Power (P)) / (Current (I))

Please note that the calculation will be performed using the given values and the formulas mentioned above.