NSC Electrical Technology Power Systems Principle and Waveforms: 3.1 Define capacitive reactance

Question

3.1 Define capacitive reactance with reference to RLC circuits.

Capacitive reactance is the opposition that a capacitor presents to the flow of alternating current (AC) in an RLC circuit. It arises from the capacitor's ability to store and release energy in an electric field, causing a phase shift between the voltage across the capacitor and the current flowing through it.

3.2 State the phase relationship between the current and voltage in a pure inductive AC circuit.

In a pure inductive AC circuit, the current lags the voltage by 90 degrees.

3.3 Refer to FIGURE 3.3 below and answer the questions that follow.
Given:
R = 60 Ω
Xc = 120 Ω
Xl = 150 Ω
Vt = 110 V
f = 60 Hz

3.3.1 Calculate the inductance of the inductor.

To find the inductance (L), we can use the formula:

$$L = \frac{X_L}{2\pi f}$$
Substituting the given values:
$$L = \frac{150}{2 	imes \pi 	imes 60} = 0.398 \, H$$

3.3.2 Calculate the impedance of the circuit.

The impedance (Z) of the circuit can be calculated using:

$$Z = \sqrt{R^2 + (X_L - X_C)^2}$$
Substituting the values:
$$Z = \sqrt{(60)^2 + (150 - 120)^2} = \sqrt{3600 + 900} = 67.08 \, \Omega$$

3.3.3 Calculate the power factor.

The power factor (PF) can be calculated using:

$$PF = \frac{R}{Z}$$
Substituting the values:
$$PF = \frac{60}{67.08} = 0.89$$

3.3.4 State THREE conditions that will occur if the power factor is at unity in an RLC series circuit.

1. The total impedance (Z) is equal to the resistance (R).
2. The phase angle between the current and the voltage is zero.
3. The voltage across the capacitor (V_C) is equal to the voltage across the inductor (V_L).

3.4 Refer to FIGURE 3.4 A and FIGURE 3.4 B to answer the questions that follow.

3.4.1 Determine the resonant frequency in FIGURE 3.4 B.

The resonant frequency (f_r) can be calculated using:
$$f_r = \frac{1}{2\pi \sqrt{LC}}$$

3.4.2 Compare the values of the inductive reactance and capacitive reactance when the frequency increases from 200 Hz to 1600 Hz.

As frequency increases, the inductive reactance increases while the capacitive reactance decreases.

3.4.3 Calculate the voltage drop across the inductor when the frequency is 600 Hz.

The voltage drop across the inductor (V_L) is:
$$V_L = I_L 	imes X_L$$

3.4.4 Calculate the value of the capacitor using the reactance value at 600 Hz.

To find the capacitance (C):
$$X_C = \frac{1}{2\pi f C}$$

3.5 Refer to FIGURE 3.5 below and answer the questions that follow.

3.5.1 Calculate the total current flow through the circuit.

At resonance, the current can be calculated using:
$$I = \frac{V_t}{Z}$$

3.5.2 Calculate the voltage drop across the inductor.

The voltage drop across the inductor (V_L) is:
$$V_L = I 	imes X_L$$

3.5.3 Calculate the Q-factor of the circuit.

The Q-factor can be calculated using:
$$Q = \frac{X_L}{R}$$

3.5.4 Explain why the phase angle of the circuit in FIGURE 3.5 would be zero.

The phase angle would be zero because $X_L$ is equal to $X_C$ and thus $V_L = V_C$ and out of phase with each other, resulting in a power factor of 1.

3.1 Define capacitive reactance with reference to RLC circuits - NSC Electrical Technology Power Systems - Question 3 - 2021 - Paper 1

Worked Solution & Example Answer:3.1 Define capacitive reactance with reference to RLC circuits - NSC Electrical Technology Power Systems - Question 3 - 2021 - Paper 1