2.1 Define the following with reference to RLC circuits: 2.1.1 Power factor 2.1.2 Q-factor of an inductor in a resonant circuit 2.2 State TWO applications of RLC circuits - NSC Electrical Technology Electronics - Question 2 - 2019 - Paper 1

The Q-factor, or quality factor, of an inductor refers to the ratio of the inductive reactance ($X_L$) to its internal resistance ($R$). This factor indicates how underdamped an oscillator or resonator is, and is calculated as follows:

Q = rac{X_L}{R}

1. RLC circuits are utilized in tuning circuits, such as radio transmitters and receivers, to select desired frequency signals while filtering out unwanted ones.

2. They are commonly used in oscillators to generate sinusoidal waveforms or in audio equipment for signal processing.

Using Kirchhoff's voltage law in the RLC circuit:

$V_T = ext{V}_R + ext{V}_L + ext{V}_C$ Substituting the values, we get: $V_T = 12 V + 16 V + 24 V = 52 V$

The inductive reactance $X_L$ can be calculated using:

X_L = rac{V_L}{I_T} = rac{16 V}{3 A} = 5.33 \, ext{Ω}

The circuit is capacitive because the voltage drop across the capacitor ($V_C = 24 V$) is greater than the voltage across the inductor ($V_L = 16 V$).

At resonance, the inductive reactance is equal to the capacitive reactance:

$X_L = X_C$

Thus,

C = rac{1}{2 imes ext{π} f X_C} = rac{1}{2 imes ext{π} imes 2000 imes 50} = 1.59 \, ext{μF}

At resonance, the total impedance $Z$ is equal to $R$, thus:

I = rac{V_T}{Z} = rac{120 V}{12 Ω} = 10 A

If the resistance is doubled, the current will be halved, due to the direct relationship between current and resistance described by Ohm's law.

1. The impedance is minimum and is equal to the resistance.
2. The current reaches its maximum value.
3. The phase angle between voltage and current is zero, indicating that they are in phase.