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

Reactance is the opposition to the change in current caused by inductors and capacitors, while impedance is the total opposition a circuit presents to alternating current, including both resistive and reactive components. Reactance is measured in ohms and can be either capacitive ( Xc) or inductive ( Xl), while impedance is the vector sum of resistance (R) and reactance (X).

The frequency/impedance characteristic curve of a series RLC circuit is typically a U-shaped graph where:

• The vertical axis represents impedance (Z) in ohms.
• The horizontal axis represents frequency (f) in Hz. At resonance (f_r), the impedance is at its minimum and equals the resistance (R). At lower frequencies, the circuit behaves inductively (Xl > Xc), and at higher frequencies, it behaves capacitively (Xc > Xl).

To calculate the Q-factor (Q) of the circuit, use the formula: $Q = \frac{X_l}{Z}$ where:

• At resonance, $X_l = X_c = 4 kΩ$,
• The total impedance $Z = R = 50 Ω$. Thus,

$Q = \frac{4000}{50} = 80$.

The inductive reactance ($X_l$) can be calculated using the formula: $X_l = 2\pi f L$ Substituting the given values: $X_l = 2\pi (50)(400 \times 10^{-3}) = 125.66 \Omega$.

The capacitive reactance ($X_c$) can be calculated using the formula: $X_c = \frac{1}{2\pi f C}$ Substituting the given values: 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 the given values: $f_r = \frac{1}{2\pi \sqrt{(400 \times 10^{-3})(47 \times 10^{-6})}} = 36.71 Hz$.