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3.1 Define phasor diagram with reference to RLC circuits connected across an alternating voltage supply - NSC Electrical Technology Power Systems - Question 3 - 2022 - Paper 1
Question 3
3.1 Define phasor diagram with reference to RLC circuits connected across an alternating voltage supply. A phasor diagram is a graphical representation of a sinusoi... show full transcript
Worked Solution & Example Answer:3.1 Define phasor diagram with reference to RLC circuits connected across an alternating voltage supply - NSC Electrical Technology Power Systems - Question 3 - 2022 - Paper 1
Step 1
3.2.1 Calculate the total supply voltage applied to the circuit.
Answer
To calculate the total supply voltage ( V_T), we can use the formula:
$$ V_T = \\sqrt{ V_R^2 + ( V_L - V_C )^2 }$$
Substituting the known values:
$$ V_T = \\sqrt{ 150^2 + (180 - 90)^2 }= \\sqrt{ 150^2 + 90^2 }$$
$$= \\sqrt{ 22500 + 8100 } = \\sqrt{ 30600 } \approx 174.93 \text{ V} $$
Step 2
3.2.2 Discuss whether the power factor will be leading or lagging.
Answer
The circuit will have a lagging power factor because the inductive voltage (V_L = 180 V) is greater than the capacitive voltage (V_C = 90 V). In an RLC circuit, when the inductive reactance exceeds the capacitive reactance, the overall current lags the voltage.
Step 3
Step 4
Step 5
3.3.3 Draw the phasor diagram for FIGURE 3.3.
Answer
To draw the phasor diagram, plot the currents I_R, I_C, and I_L on a graph where I_R lies along the horizontal axis. From the tip of I_R, draw I_C vertically upwards since it's a capacitive current. The inductive current I_L will be drawn at an angle to reflect the phase angle calculated. Label the relevant angles and current vectors.
Step 6
3.3.4 Motivate with a reason if the circuit is predominately capacitive or inductive.
Answer
The circuit is predominantly inductive because the inductive current (I_L = 6 A) is greater than the capacitive current (I_C = 4 A). This suggests that the circuit behavior is influenced more by the inductor.
Step 7
Step 8
Step 9
3.4.3 Calculate the value of the capacitor.
Answer
To find the capacitance (C), we can use:
$$ X_C = \frac{1}{2 \pi f_r C} $$
Rearranging gives us:
$$ C = \frac{1}{2 \pi f_r X_C} $$
Substituting the known values:
$$ C = \frac{1}{2 \pi \times 2,387 \times 10^3 \times 150} \approx 444.51 \mu F $$
Step 10
3.4.4 Define the term selectivity with reference to resonant circuits.
Answer
Selectivity is a measure of how well a resonant circuit responds to a range of frequencies and excludes others. It describes the circuit’s ability to effectively isolate a specific frequency from adjacent frequencies.
Step 11
3.5.1 State with a reason the type of component that produces the waveform in FIGURE 3.5 (A).
Answer
The type of component that produces the waveform in FIGURE 3.5 (A) is an inductor because the voltage waveform lags behind the current waveform, which is characteristic of inductive components.
Step 12
3.5.2 Identify the power source and power dissipated in FIGURE 3.5 (B). Motivate your answer.
Answer
In FIGURE 3.5 (B), the power source is the alternating voltage supply, while the power dissipated is the average power, indicated by the area under the voltage and current curves. The difference between the peak values and the average indicates the efficiency of power usage in the circuit.