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

For FIGURE 3.2.1, the phasor for voltage ( $V_R$) leads the current phasor by 90 degrees, while in FIGURE 3.2.2, the phasor for capacitive voltage ( $V_C$) lags behind the current by 90 degrees.

The impedance $Z$ in a series circuit is calculated using the formula:
$Z = \\sqrt{R^2 + (X_L - X_C)^2}$
Substituting the given values: $Z = \\sqrt{25^2 + (94 - 13)^2} = \\sqrt{25^2 + 81^2} = 84.77 \Omega$

The phase angle $heta$ can be calculated using the formula:
$\cos \theta = \frac{R}{Z}$
Thus, $\cos \theta = \frac{25}{84.77} \\Rightarrow \theta = \cos^{-1}(0.294) \\Rightarrow 72.86°$

The value of the inductor $L$ can be found using the formula: $L = \frac{X_L}{2 \pi f}$ Substituting the values, we have: $L = \frac{94}{2 \times 3.14 \times 60} = 0.25 H = 250 mH$

A lagging power factor occurs in an RLC circuit when the current lags behind the voltage. This is typically observed in circuits with inductance, where the inductive reactance dominates.

In a series RLC resonance circuit, the inductive and capacitive reactances cancel each other out, resulting in a purely resistive circuit at the resonant frequency. Consequently, the current and voltage waveforms become in phase.

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

The power factor can be calculated using: $\cos \theta = \frac{I_R}{I_T}$ Thus: $\cos \theta = \frac{11}{11.18} = 0.98$

The total power $P$ in the circuit is given by: $P = V_T \times I_T \times \cos \theta$ Substituting the values: $P = 110 \times 11.18 \times 0.98 = 1205.20 W = 1.21 kW$

The circuit has a lagging power factor because the inductive current is greater than the capacitive current.

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

Impedance is the total opposition that a circuit offers to the flow of alternating current, measured in ohms, while current is the flow of electric charge in a circuit, measured in amperes.

As frequency increases, the impedance exhibits a resonant peak at the resonant frequency. Below the resonant frequency, impedance is mostly inductive, while above it, impedance becomes capacitive, causing a decrease in total impedance.