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. 2.3 FIGURE 2.3 below shows an RLC series circuit. Answer the questions that follow. Given: I_T = 3 A V_R = 12 V V_L = 16 V V_C = 24 V f = 60 Hz 2.3.1 Calculate the total voltage of the supply. 2.3.2 Calculate the value of the inductive reactance. 2.3.3 State if the circuit is capacitive or inductive. Motivate your answer. 2.3.4 Complete the phasor diagram on the ANSWER SHEET for QUESTION 2.3.4 and show the direction of rotation. 2.3.5 Describe how an increase in impedance, while keeping the resistance constant, will affect the phase angle and the power factor. 2.4 FIGURE 2.4 below shows an RLC parallel circuit consisting of a 20 Ω resistor, an inductor with an inductive reactance of 30 Ω and a capacitor with a capacitive reactance of 40 Ω, all connected across a 120 V/60 Hz supply. Answer the questions that follow. Given: R = 20 Ω X_L = 30 Ω X_C = 40 Ω f = 60 Hz 2.4.1 Calculate the total current in the circuit. 2.4.2 Calculate the phase angle. 2.4.3 State whether the phase angle is leading or lagging. Motivate your answer. 2.5 FIGURE 2.5 below shows an RLC series resonant circuit which consists of a 12 Ω resistor, an inductor with an inductive reactance of 50 Ω and a variable capacitor, all connected across a 120 V/2 kHz supply. Answer the questions that follow. Given: R = 12 Ω X_L = 50 Ω 2.5.1 Calculate the value of C when the circuit resonates at 2 kHz. 2.5.2 Calculate the value of the current in the circuit. 2.5.3 State how current will be affected if the resistance is doubled. 2.5.4 List THREE characteristics of an RLC series circuit at resonance.

NSC Electrical Technology Power Systems Applications and Diagrams: 2.1 Define the following with re

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 Power Systems - Question 2 - 2019 - Paper 1

Question 2

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... show full transcript

Worked Solution & Example Answer: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 Power Systems - Question 2 - 2019 - Paper 1

Step 1

2.1.1 Power factor

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The power factor is the ratio of the true power (measured in watts) to the apparent power (measured in volt-amperes) in an AC circuit. Mathematically, it can be represented as:

ext{Power Factor} = rac{P}{S}

where P is the real power and S is the apparent power.

Step 2

2.1.2 Q-factor of an inductor in a resonant circuit

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The Q-factor, or quality factor, of an inductor in a resonant circuit measures the inductor's efficiency. It is defined as the ratio of its inductive reactance to its internal resistance:

Q = rac{X_L}{R}

where $X_L$ is the inductive reactance.

Step 3

2.2 State TWO applications of RLC circuits

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RLC circuits are used in radio receivers to tune into specific frequencies.
They are also used in filter circuits to allow certain frequency ranges to pass while attenuating others.

Step 4

2.3.1 Calculate the total voltage of the supply

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To calculate the total voltage of the supply, use the formula:

V_T = ext{√}ig(V_C^2 + (V_L - V_R)^2ig)

Substituting the values:

V_T = ext{√}ig(24^2 + (16 - 12)^2ig) = ext{√}(576 + 16) = ext{√}592 = 24.4 V

Step 5

2.3.2 Calculate the value of the inductive reactance

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The inductive reactance $X_L$ can be calculated using the formula:

X_L = I_L imes R

Here,

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

Step 6

2.3.3 State if the circuit is capacitive or inductive. Motivate your answer.

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The circuit is capacitive because the voltage drop across the capacitor ( $V_C = 24 V$ ) is greater than the voltage across the inductor ( $V_L = 16 V$ ). Therefore, the behavior of the circuit is primarily influenced by the capacitor.

Step 7

2.4.1 Calculate the total current in the circuit

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The total current in the circuit can be calculated using:

I_T = ext{√}ig(I_R^2 + (I_L - I_C)^2ig)

Given the values:

I_T = ext{√}ig(6^2 + (6 - 3)^2ig) = ext{√}(36 + 9) = ext{√}45 = 6.08 A

Step 8

2.4.2 Calculate the phase angle

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The phase angle $heta$ can be calculated using:

heta = ext{Cos}^{-1}igg( rac{I_R}{I_T}igg)

Substituting the known values:

heta = ext{Cos}^{-1}igg( rac{6}{6.08}igg) ightarrow ≈ 9.30°

Step 9

2.4.3 State whether the phase angle is leading or lagging. Motivate your answer.

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The phase angle is lagging because the inductive current ( $I_L$ ) is greater than the capacitive current ( $I_C$ ). This indicates that the inductive component is dominant in the circuit.

Step 10

2.5.1 Calculate the value of C when the circuit resonates at 2 kHz

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At resonance, $X_L = X_C$ . The resonance condition in terms of capacitance can be given by:

C = rac{1}{2 ext{π}f X_L}

Substituting for f = 2000 Hz and $X_L = 50 ext{ Ω}$ :

C = rac{1}{2 imes 3.14 imes 2000 imes 50} = 16 ext{ μF}

Step 11

2.5.2 Calculate the value of the current in the circuit

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At resonance, the impedance Z equals the resistance R:

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

Step 12

2.5.3 State how current will be affected if the resistance is doubled.

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If the resistance is doubled, the current will be halved. This is because the total impedance will increase, thereby reducing the current according to Ohm's law.

Step 13

2.5.4 List THREE characteristics of an RLC series circuit at resonance.

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The impedance is at a minimum, equal only to the resistance R.
The phase angle is zero degrees, meaning voltage and current are in phase.
The current is at its maximum value.

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 Power Systems - Question 2 - 2019 - Paper 1

Worked Solution & Example Answer: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 Power Systems - Question 2 - 2019 - Paper 1

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

2.3.1 Calculate the total voltage of the supply

2.3.2 Calculate the value of the inductive reactance

2.3.3 State if the circuit is capacitive or inductive. Motivate your answer.

2.4.1 Calculate the total current in the circuit

2.4.2 Calculate the phase angle

2.4.3 State whether the phase angle is leading or lagging. Motivate your answer.

2.5.1 Calculate the value of C when the circuit resonates at 2 kHz

2.5.2 Calculate the value of the current in the circuit

2.5.3 State how current will be affected if the resistance is doubled.

2.5.4 List THREE characteristics of an RLC series circuit at resonance.

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