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 offered by a specific reactive component (capacitor or inductor) to the flow of current in AC circuits. It depends on the frequency and the value of the reactive component.

Impedance is the total opposition offered to the flow of current in an AC circuit, which includes both resistive and reactive components (i.e., resistance and reactance).

The typical frequency/impedance characteristic curve is a downward-sloping curve that crosses the impedance axis (Z) at the resonant frequency ($f_r$). The X-axis represents the frequency (F [Hz]), while the Y-axis represents the impedance (Z [Ω]). At resonance, the impedance is at its minimum value, and the relation shown in the graph indicates that for frequencies below $f_r$, the circuit behaves more inductively, and for frequencies above $f_r$, it behaves more capacitively.

The Q-factor (Quality factor) is calculated using the formula:

$Q = \frac{X_L}{Z}$

Where:

• $X_L$ = Inductive reactance = 4 kΩ
• $Z$ = Total impedance = 50 Ω

Plugging in the values gives us: $Q = \frac{4000}{50} = 80$

To calculate the inductive reactance ($X_L$), we use the formula:

$X_L = 2\pi f L$

Where:

• $f = 50 Hz$
• $L = 400 mH = 0.4 H$

Substituting the values: $X_L = 2\pi (50)(0.4) \approx 125.66 \Omega$

To find the capacitive reactance ($X_C$), we use:

$X_C = \frac{1}{2\pi f C}$

Where:

• $C = 47 μF = 47 \times 10^{-6} F$

Substituting the values: $X_C = \frac{1}{2\pi (50)(47 \times 10^{-6})} \approx 67.73 \Omega$

The resonant frequency ($f_r$) for a series RLC circuit is calculated as:

$f_r = \frac{1}{2\pi \sqrt{LC}}$

Where:

• $L = 400 mH = 0.4 H$
• $C = 47 μF = 47 \times 10^{-6} F$

Substituting the values: $f_r = \frac{1}{2\pi \sqrt{(0.4)(47 \times 10^{-6})}} \approx 36.71 Hz$