5.1 Name the TWO factors that influence the reactance of a capacitor - NSC Electrical Technology Power Systems - Question 5 - 2016 - Paper 1

Reactance is the opposition of the specific reactive component to the flow of current in AC circuits, while impedance is the total opposition offered to the flow of current in an AC circuit which contains both resistive and reactive components.

The characteristic curve of a series RLC circuit typically shows impedance (Z) on the vertical axis and frequency (f) on the horizontal axis. As frequency increases, impedance generally decreases until it reaches a minimum point at the resonant frequency (f_r), after which it starts to rise again. The resonant point indicates the frequency where the circuit’s inductive and capacitive reactances are equal.

Given that at resonance, the inductive reactance (X_L) and capacitive reactance (X_C) are both equal to 4 kΩ, and knowing that the circuit includes a series resistance (R) of 50 Ω, the Q-factor can be calculated using the formula: $Q = \frac{X_L}{Z}$ where Z is the total impedance. Thus, we find: $Q = \frac{4000}{50} = 80$.

The inductive reactance (X_L) can be calculated using the formula: $X_L = 2\pi f L$ where f = 50 Hz and L = 400 mH. Therefore: $X_L = 2\pi (50)(400 \times 10^{-3}) = 125.66 \Omega$.

The capacitive reactance (X_C) can be calculated using the formula: $X_C = \frac{1}{2\pi f C}$ where f = 50 Hz and C = 47 μF. Thus: X_C = \frac{1}{2\pi (50)(47 \times 10^{-6}) = 67.73 \Omega.

The resonant frequency (f_r) can be calculated using the formula: $f_r = \frac{1}{2\pi \sqrt{LC}}$ Substituting L = 400 mH and C = 47 μF: $f_r = \frac{1}{2\pi \sqrt{(400 \times 10^{-3})(47 \times 10^{-6})}} = 36.71 Hz.$ This shows the frequency at which the circuit will resonate.