Question

Помогите решить физику срочно В сеть переменного тока частотой 50 Гц последовательно включены активное сопротивление и катушка индуктивности. Напряжение U=500 В, сопротивление R=20 Ом, индуктивность катушки L=54 мГн. Определить: полное сопротивление, ток, напряжения на индуктивности и активном сопротивлении, коэффициент мощности, угол сдвига фаз, полную, активную и реактивную мощность. Построить векторную диаграмму. Написать выражения для мгновенных значений тока и напряжения.

Answer 1

Ответ:

Объяснение:

Дано:

f = 50 Гц

U = 500 В

R = 20 Ом

L = 54 мГн = 54·10⁻³ Гн

_____________

Z - ?

I - ?

Uс - ?

UL - ?

cos φ - ?

P - ?

Q - ?

S - ?

1)

Сопротивление катушки:

XL = 2π·f·L = 2·3,14·50·54·10⁻³ ≈ 17 Ом

Полное сопротивление:

Z = √ (R² + XL²) = √ (20² + 17²) ≈ 26 Ом

2)

Сила тока:

I = U / Z = 500 / 26 ≈ 19 А

3)

Напряжения:

UR = R·I = 20·19 = 380 В

UL = XL·I = 17·19 ≈ 320 В

4)

Коэффициент мощности

cos φ = R / Z = 20 / 26 ≈ 0,77

5)

Угол сдвига фаз:

φ = arccos 0,77 ≈ 40°

6)

Мощности:

P = U·I · cos φ = 500·19·0,77 ≈ 7 300 Вт

Q = U·I·sin φ = 500·19·0,6428 ≈ 6 100 вар

S = U·I = 500·19 = 9 500 В·А

Answer 2

Given Information

In the circuit, there is an active resistance (R) and an inductance coil (L) connected in series to a 50 Hz AC power supply. The voltage (U) across the circuit is 500 V, the resistance (R) is 20 Ω, and the inductance (L) of the coil is 54 mH.

Calculating Total Impedance

To determine the total impedance (Z) of the circuit, we can use the formula:

Z = √(R^2 + (ωL)^2)

where ω is the angular frequency and is given by ω = 2πf, where f is the frequency of the AC power supply.

Substituting the given values into the formula, we get:

Z = √(20^2 + (2π * 50 * 0.054)^2)

Calculating this expression will give us the total impedance of the circuit.

Calculating Current

The current (I) flowing through the circuit can be calculated using Ohm's Law:

I = U / Z

where U is the voltage across the circuit and Z is the total impedance.

Substituting the given values into the formula, we get:

I = 500 / Z

Calculating this expression will give us the current flowing through the circuit.

Calculating Voltages

To calculate the voltages across the inductance coil and the active resistance, we can use the formulas:

Voltage across inductance (UL) = I * ωL

Voltage across resistance (UR) = I * R

where I is the current flowing through the circuit, ω is the angular frequency, L is the inductance, and R is the resistance.

Substituting the given values into the formulas, we get:

UL = I * 2π * 50 * 0.054

UR = I * 20

Calculating these expressions will give us the voltages across the inductance coil and the active resistance.

Calculating Power Factors and Phase Shift

The power factor (PF) and the phase shift (θ) can be calculated using the formulas:

Power Factor (PF) = cos(θ) = UR / U

Phase Shift (θ) = arccos(PF)

where UR is the voltage across the resistance and U is the total voltage across the circuit.

Substituting the given values into the formulas, we get:

PF = UR / U

θ = arccos(PF)

Calculating these expressions will give us the power factor and the phase shift.

Calculating Total, Active, and Reactive Power

The total power (P), active power (P_active), and reactive power (P_reactive) can be calculated using the formulas:

Total Power (P) = U * I * PF

Active Power (P_active) = U * I * cos(θ)

Reactive Power (P_reactive) = U * I * sin(θ)

where U is the total voltage across the circuit, I is the current flowing through the circuit, PF is the power factor, and θ is the phase shift.

Substituting the given values into the formulas, we get:

P = U * I * PF

P_active = U * I * cos(θ)

P_reactive = U * I * sin(θ)

Calculating these expressions will give us the total power, active power, and reactive power.

Vector Diagram

To construct a vector diagram, we can represent the voltage across the resistance (UR) and the voltage across the inductance (UL) as vectors. The total voltage (U) can be represented as the vector sum of UR and UL. The angle between the total voltage vector and the resistance voltage vector represents the phase shift (θ).

Instantaneous Values of Current and Voltage

The instantaneous values of current (i) and voltage (u) can be expressed as sinusoidal functions of time. For an AC circuit with a frequency of 50 Hz, the general expressions are:

i(t) = I * sin(ωt + φ)

u(t) = U * sin(ωt)

where I is the amplitude of the current, U is the amplitude of the voltage, ω is the angular frequency, t is the time, and φ is the phase angle.

Substituting the given values into the expressions, we can obtain the instantaneous values of current and voltage.

Please note that the calculations and expressions provided above are based on the given information and assumptions.