2.1 Define the term impedance with reference to RLC circuits - NSC Electrical Technology Electronics - Question 2 - 2018 - Paper 1

The waveform for a pure capacitive circuit shows the voltage waveform leading the current waveform by 90 degrees. The graph would illustrate the voltage (V_C) reaching its peak a quarter cycle before the current (I) waveform reaches its peak.

In a pure inductive circuit, the current lags the voltage by 90 degrees. The graph would depict the voltage (V_L) at its peak a quarter cycle ahead of the current (I) waveform's peak.

Given the reactance of the capacitor (X_C = 36 Ω) and the frequency (f = 60 Hz), the capacitance can be calculated as follows:

$C = \frac{1}{2 \pi f X_C} = \frac{1}{2 \pi \times 60 \times 36} = 73.68 \mu F$

The inductance can be calculated with the formula: $L = \frac{X_L}{2\pi f} = \frac{22}{2\pi \times 60} = 58.35 mH$

The total impedance can be found using the formula: $Z = \sqrt{R^2 + (X_L - X_C)^2} = \sqrt{12^2 + (22 - 36)^2} = 18.44 \Omega$

Using Ohm's law, the current can be determined by: $I = \frac{V_s}{Z} = \frac{60}{18.44} = 3.25 A$

The Quality Factor can be calculated using: $Q = \frac{V_s}{I \times Z} = \frac{60}{3.25 \times \sin(50^\circ)} = 149.38 VA$

The value of the inductive reactance will increase with an increase in frequency due to the formula: $X_L = 2\pi f L$. As the frequency rises, the overall inductive reactance also rises, which affects the circuit’s impedance.

Resonance occurs in an RLC circuit when the inductive reactance equals the capacitive reactance, resulting in a maximum current flow at a certain frequency known as the resonant frequency.