2.1 Define the following terms: 2.1.1 Capacitive reactance 2.1.2 Inductive reactance 2.2 FIGURE 2.2 below represents an RLC series circuit that consists of a 25 Ω resistor, a 44 mH inductor and a 120 μF capacitor, all connected across a 120 V/60 Hz supply - NSC Electrical Technology Power Systems - Question 2 - 2019 - Paper 1

Inductive reactance is defined as the opposition to an alternating current by the reactive component of an inductor in an AC circuit. It can be calculated using the formula:

$X_L = 2 \pi f L$

To calculate the inductive reactance, we use:

$X_L = 2 \pi f L$

Substituting the given values:

$X_L = 2 \pi (60)(44 \times 10^{-3}) = 16.59 \, \Omega$

To calculate the capacitive reactance, we use:

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

Substituting the given values:

$X_C = \frac{1}{2 \pi (60)(120 \times 10^{-6})} = 22.11 \, \Omega$

To find the impedance, we utilize the formula:

$Z = \sqrt{R^2 + (X_C - X_L)^2}$

Substituting the calculated values:

$Z = \sqrt{(25)^2 + (22.11 - 16.59)^2} = 25.6 \, \Omega$

The current through the capacitor can be calculated using:

$I_C = \frac{V_S}{X_C}$

Substituting the values:

$I_C = \frac{220}{60} = 3.67 \, A$

To calculate the reactive current, we use:

$I_L = I_T - I_C$

Given that $I_T = 6 \, A$:

$I_L = 6 - 3.67 = 2.33 \, A$

The phase angle is leading because the current through the capacitor leads the voltage across it in an AC circuit. Capacitive circuits result in a leading phase angle.

At resonance, capacitive reactance $X_C$ equals inductive reactance $X_L$. Therefore, the value is simply equal to $X_L$.

To calculate the value of the capacitor at resonance, we use:

$C = \frac{1}{(2 \pi f X_L)}$

Substituting for $f = 1000 \, Hz$ and $X_L = 50.27 \Omega$:

$C = \frac{1}{2 \pi (1000)(50.27)} = 3.16 \times 10^{-5} \, F\, (31.6 \mu F)$

At resonance, the circuit behaves as a purely resistive circuit, and the current is maximum due to the impedance being minimized (only the resistance). If the supply voltage increases, the current will increase proportionally.