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. Answer the questions that follow. Calculate the: 2.2.1 Inductive reactance 2.2.2 Capacitive reactance 2.2.3 Impedance of the circuit 2.3 FIGURE 2.3 below shows an RLC parallel circuit that consists of a 40 Ω resistor, an inductor with unknown inductance and a capacitor with a capacitive reactance of 60 Ω, all connected across a 220 V/60 Hz supply. Answer the questions that follow. Calculate the: 2.3.1 the current through the capacitor. 2.3.2 Calculate the reactive current. 2.3.3 State, with a reason, whether the phase angle is leading or lagging. 2.4 FIGURE 2.4 below shows an RLC series circuit that consists of a 12 Ω resistor, an inductor and a variable capacitor connected across a 120 V AC supply. The circuit resonates at 1 kHz. Answer the questions that follow. 2.4.1 State the value of the capacitive reactance at resonance. 2.4.2 Calculate the value of the capacitor at resonance. 2.4.3 Explain how the value of the current can be affected by the voltage across the inductor being greater than the supply voltage.

NSC Electrical Technology Power Systems Concepts and Calculations: 2.1 Define the following terms:

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

Question 2

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... show full transcript

Worked Solution & Example Answer: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

Step 1

2.1.1 Capacitive reactance

96%

114 rated

Answer

Capacitive reactance (denoted by $X_C$ ) is defined as the opposition to alternating current by the reactive component of a capacitor in an AC circuit. It can be mathematically expressed as:

$X_C = rac{1}{2 imes au imes f imes C}$

where $au$ is the time constant, $f$ is the frequency, and $C$ is the capacitance in farads.

Step 2

2.1.2 Inductive reactance

99%

104 rated

Answer

Inductive reactance (denoted by $X_L$ ) is the opposition to alternating current by the reactive component of an inductor in an AC circuit. It can be expressed with the following formula:

$X_L = 2 imes au imes f imes L$

where $L$ is the inductance in henries.

Step 3

2.2.1 Inductive reactance

96%

101 rated

Answer

To calculate the inductive reactance:

Using the formula:

$X_L = 2 imes au imes f imes L$ Substituting the given values:

$X_L = 2 imes 3.14159 imes 60 imes 0.044 = 16.59 ext{ Ω}$

Step 4

2.2.2 Capacitive reactance

98%

120 rated

Answer

To calculate the capacitive reactance:

Using the formula:

$X_C = rac{1}{2 imes au imes f imes C}$ Substituting the given values:

$X_C = rac{1}{2 imes 3.14159 imes 60 imes 120 imes 10^{-6}} = 22.11 ext{ Ω}$

Step 5

2.2.3 Impedance of the circuit

97%

117 rated

Answer

To find the impedance of the circuit, use the formula:

ewline \\ \\ \\ \\ \\\ \\\ \\ \\ \\ Z = ewline \\ \\ R + j(X_L - X_C)$$ Calculating: $$Z = ewline \\ \\ \\ \\ \\ = ewline \\ \\\ \\ \\ \\Z = ewline \\ \\ \\ = ewline \\25 ext{Ω}^2 + (22.11 - 16.59) ^ 2$$ Evaluating: $$Z = 25.6 Ω$$

Step 6

2.3.1 the current through the capacitor.

97%

121 rated

Answer

To find the current through the capacitor, use:

$I_C = rac{V_s}{X_C}$ Substituting:

$I_C = rac{220}{60} = 3.67 A$

Step 7

2.3.2 Calculate the reactive current.

96%

114 rated

Answer

The reactive current ( $I_L$ ) through the inductor can be found by:

$I_L = I_t - I_C$ Given $I_t = 6 A$ :

$I_L = 6 - 3.67 = 2.33 A$

Step 8

2.3.3 State, with a reason, whether the phase angle is leading or lagging.

99%

104 rated

Answer

In an RLC circuit, if the capacitive current is higher than the inductive current, the voltage across the capacitor leads the current; thus, the phase angle is leading. Conversely, if the inductive current dominates, the phase angle lags.

Step 9

2.4.1 State the value of the capacitive reactance at resonance.

96%

101 rated

Answer

At resonance in an RLC circuit, the capacitive reactance ( $X_C$ ) equals the inductive reactance ( $X_L$ ). Therefore, this state results in:\n $X_C = X_L$

Step 10

2.4.2 Calculate the value of the capacitor at resonance.

98%

120 rated

Answer

Using the formula at resonance:

$f = rac{1}{2 au ext{C}}$ Rearranging gives:

$C = rac{1}{2 imes au imes f} = rac{1}{2 imes 3.14159 imes 1000} = 159.15 ext{ μF}$

Step 11

2.4.3 Explain how the value of the current can be affected by the voltage across the inductor being greater than the supply voltage.

97%

117 rated

Answer

In a series RLC circuit, the voltage across the inductor can be greater than the supply voltage due to resonance effects. When this occurs, it can lead to increased current through the circuit as the total impedance decreases, causing a rise in voltage across the inductor as compared to the supply voltage.

2.1.1 Capacitive reactance

2.1.2 Inductive reactance

2.2.1 Inductive reactance

2.2.2 Capacitive reactance

2.2.3 Impedance of the circuit

2.3.1 the current through the capacitor.

2.3.2 Calculate the reactive current.

2.3.3 State, with a reason, whether the phase angle is leading or lagging.

2.4.1 State the value of the capacitive reactance at resonance.

2.4.2 Calculate the value of the capacitor at resonance.

2.4.3 Explain how the value of the current can be affected by the voltage across the inductor being greater than the supply voltage.

Join the NSC students using SimpleStudy...