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2.2.1 Calculate the inductive reactance of the inductor - NSC Electrical Technology Power Systems - Question 2 - 2020 - Paper 1
Question 2
2.2.1 Calculate the inductive reactance of the inductor. 2.2.2 Calculate the voltage drop across the capacitor. 2.2.3 Indicate whether the supply voltage is lagg... show full transcript
Worked Solution & Example Answer:2.2.1 Calculate the inductive reactance of the inductor - NSC Electrical Technology Power Systems - Question 2 - 2020 - Paper 1
Step 1
Calculate the inductive reactance of the inductor.
Answer
The inductive reactance ( X_L) can be calculated using the formula:
Given:
- Frequency ( f) = 60 Hz
- Inductance ( L) = 300 mH = 300 \times 10^{-3} H
Plugging in the values, we have:
Thus, the inductive reactance is approximately 56.55 Ω.
Step 2
Calculate the voltage drop across the capacitor.
Answer
The voltage drop across the capacitor ( V_C) can be calculated using:
To find X_C:
Where:
- Capacitance ( C) = 150 μF = 150 \times 10^{-6} F
Calculating X_C:
Using the current through the capacitor ( I_C), which can be derived from the total circuit current, we can now determine:
Thus, if I_C is known, V_C can be calculated.
Step 3
Indicate whether the supply voltage is lagging or leading. Motivate your answer.
Answer
The supply voltage is leading because the capacitive reactance ( X_C) is smaller than the inductive reactance ( X_L). In an RLC circuit, when the capacitive reactance is greater, the resultant current leads the voltage across the source. Therefore, since X_C is less than X_L, the circuit is predominantly capacitive, and the supply voltage leads the supply current.
Step 4
Draw the phasor diagram of the circuit on the ANSWER SHEET FOR QUESTION 2.2.4.
Answer
The phasor diagram represents the relationship between the different voltages (Phase voltages across R, L, and C) and the supply voltage. In the diagram:
- The current ( I_T) will be shown as the reference phasor.
- The voltage across the resistor ( V_R) will be in phase with the current.
- The voltage across the inductor ( V_L) will lag behind the current by 90 degrees.
- The voltage across the capacitor ( V_C) will lead the current by 90 degrees.
- The supply voltage ( V_X) will be the vector sum of these voltages.