3.1 Explain the term inductance with reference to RLC circuits connected to an AC supply - NSC Electrical Technology Electronics - Question 3 - 2022 - Paper 1

Phasor diagram for figure 3.2.1 shows the voltage ( V_R) leading the current (I) by 90° indicating resistive load. Phasor diagram for figure 3.2.2 shows the voltage ( V_C) lagging the current by 90°, indicating capacitive load.

To calculate the impedance (Z) of the circuit, we use the formula: $Z = \\sqrt{R^2 + (X_L - X_C)^2}$ Substituting the given values: $Z = \\sqrt{25^2 + (94 - 13)^2} \\approx 84.77 \, \Omega$

The phase angle (θ) can be calculated using the formula: $\theta = \cos^{-1} \left( \frac{R}{Z} \right)$ Substituting the values: $\theta = \cos^{-1} \left( \frac{25}{84.77} \right) \approx 72.85°$

The inductance (L) can be calculated using the formula: $L = \frac{X_L}{2 \pi f}$ Substituting the values: $L = \frac{94}{2 \times \pi \times 60} \approx 0.25 \, H$. Therefore, the value of the inductor is 250 mH.

A lagging power factor occurs when the current in an AC circuit lags behind the voltage. This is common in inductive circuits, where the inductor delays the current's peak compared to the voltage's peak.

In a series RLC resonance circuit, the inductive reactance (X_L) and capacitive reactance (X_C) cancel each other out at the resonant frequency. This results in a purely resistive impedance, causing the current and voltage waveforms to be in phase.

The total current (I_T) in the circuit can be calculated using the formula: $I_T = \\sqrt{(I_L - I_C)^2 + I_R^2}$ Substituting the values: $I_T = \\sqrt{(9 - 7)^2 + 11^2} = 11.18 \, A$

The power factor (PF) is calculated using the formula: $PF = \frac{I_R}{I_T} = \frac{11}{11.18} \approx 0.98$

The total power (P) can be found using: $P = V_T \times I_T \times PF = 110 \times 11.18 \times 0.98 \approx 1205.2 \, W \text{ or } 1.21 \, kW$

The circuit has a lagging power factor because the inductive current (I_L) is greater than the capacitive current (I_C), indicating that the current lags behind the voltage.

The circuit that produces the response at A and B in FIGURE 3.5 is a parallel RLC circuit.

Impedance refers to the total opposition that a circuit offers to the flow of alternating current, while the current is the flow of charge through the circuit. Impedance can be maximum at certain frequencies, while current will be minimum in those conditions.

As the frequency increases, the impedance initially decreases to a minimum at the resonant frequency and then increases again beyond this point. This reflects the relationship between inductive and capacitive reactance in the circuit.