Question

Индуктивное и активное сопротивление катушки составляет соответственно 12 и 5 Ом. Действующее значение при преложенного к ней напряжения U=110 B. Построить векторную диаграмму и треугольник мощностей.

Answer 1

См. рисунок .......,,,

Answer 2

Calculation of Inductive and Active Resistance

To calculate the inductive and active resistance of a coil, we are given that the inductive resistance is 12 Ω and the active resistance is 5 Ω. Additionally, the applied voltage to the coil is U = 110 V.

Vector Diagram

To construct the vector diagram, we need to consider the inductive and active components of the coil's impedance. The inductive component is represented by the reactance (X) and the active component is represented by the resistance (R).

The reactance (X) can be calculated using the formula: X = 2πfL, where f is the frequency and L is the inductance.

Since the frequency is not provided, we will assume it to be 50 Hz for the purpose of this example.

Using the given inductive resistance of 12 Ω, we can calculate the inductance (L) using the formula: XL = 2πfL, where XL is the inductive reactance.

Let's calculate the inductance (L): 12 Ω = 2π(50 Hz)L

Simplifying the equation, we find: L ≈ 0.381 H

Now that we have the inductance, we can calculate the reactance (X): X = 2π(50 Hz)(0.381 H)

Simplifying the equation, we find: X ≈ 119.38 Ω

The vector diagram represents the impedance of the coil as a phasor. The length of the phasor represents the magnitude of the impedance, and the angle represents the phase difference between the voltage and current.

To construct the vector diagram, we draw a horizontal line to represent the real part (active resistance) and a vertical line to represent the imaginary part (inductive reactance). The hypotenuse of the right triangle formed represents the impedance.

Power Triangle

The power triangle represents the relationship between the active power (P), reactive power (Q), and apparent power (S) in an AC circuit.

The active power (P) can be calculated using the formula: P = UI cos(θ), where U is the voltage and θ is the phase angle between the voltage and current.

The reactive power (Q) can be calculated using the formula: Q = UI sin(θ)

The apparent power (S) can be calculated using the formula: S = UI

Let's calculate the power values using the given voltage of 110 V.

The active power (P) is given by: P = 110 V * 5 Ω * cos(θ)

The reactive power (Q) is given by: Q = 110 V * 119.38 Ω * sin(θ)

The apparent power (S) is given by: S = 110 V * (5 Ω + 119.38 Ω)

Conclusion

To summarize, we have calculated the inductive and active resistance of the coil, constructed the vector diagram representing the impedance, and calculated the power values using the given voltage.

Please note that the frequency was assumed to be 50 Hz for the purpose of this example. The actual frequency may affect the calculations.

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