Characteristics of Thyristor MCQ Quiz in தமிழ் - Objective Question with Answer for Characteristics of Thyristor - இலவச PDF ஐப் பதிவிறக்கவும்

\(\begin{array}{l} \omega = \sqrt {\frac{1}{{LC}} - \frac{{{R^2}}}{{4{L^2}}}} \\ = \sqrt {\frac{1}{{10 \times {{10}^{ - 3}} \times 10 \times {{10}^{ - 6}}}} - \frac{{{{\left( {60} \right)}^2}}}{{4{{\left( {10 \times {{10}^{ - 3}}} \right)}^2}}}} \end{array}\)

= 1000 rad / sec

Conduction time of SCR \( = \frac{\pi }{\omega } = \frac{\pi }{{1000}}\)

= 3.14 msec.

Irrespective of thyristor ratings, latching current is 1.5 to 2 times that of holding current. Hence option (b) is correct.

Explanation:

Distortion Factor (DF) and Total Harmonic Distortion (THD) Relationship

Definition: Distortion factor (DF) and total harmonic distortion (THD) are metrics used to quantify the distortion in a waveform, typically an electrical signal, caused by the presence of harmonics. These metrics are vital in analyzing the quality of an electrical signal in power systems, audio applications, and communication systems.

The distortion factor (DF) is a measure of the waveform's deviation from a pure sine wave due to harmonics, while total harmonic distortion (THD) quantifies the extent of harmonic distortion as a ratio of the harmonic content to the fundamental frequency.

Correct Formula:

The relationship between DF and THD is given by the formula:

\(\mathrm{DF} = \sqrt{\frac{1}{1+\mathrm{THD}^{2}}}\)

This formula (Option 2) correctly relates DF and THD. It signifies that the distortion factor decreases as the total harmonic distortion increases, reflecting the increasing deviation of the waveform from a pure sine wave.

Derivation:

To derive the relationship between DF and THD:

• Let the fundamental frequency component of the waveform be \(V_1\), and the RMS value of the harmonic components be \(V_{\text{harmonics}}\).
• The total RMS value of the waveform, \(V_{\text{total}}\), is given by: \[ V_{\text{total}} = \sqrt{V_1^2 + V_{\text{harmonics}}^2} \]
• Total harmonic distortion (THD) is defined as: \[ \mathrm{THD} = \frac{V_{\text{harmonics}}}{V_1} \] Substituting \(V_{\text{harmonics}} = \mathrm{THD} \cdot V_1\) into the total RMS equation: \[ V_{\text{total}} = \sqrt{V_1^2 + (\mathrm{THD} \cdot V_1)^2} = V_1 \sqrt{1 + \mathrm{THD}^2} \]
• The distortion factor (DF) is defined as the ratio of \(V_1\) to \(V_{\text{total}}\): \[ \mathrm{DF} = \frac{V_1}{V_{\text{total}}} = \frac{V_1}{V_1 \sqrt{1 + \mathrm{THD}^2}} = \sqrt{\frac{1}{1 + \mathrm{THD}^2}} \]

Thus, the formula \(\mathrm{DF} = \sqrt{\frac{1}{1+\mathrm{THD}^{2}}}\) is derived, confirming Option 2 as the correct answer.

Applications:

• Analyzing power system quality in electrical grids.
• Evaluating signal quality in audio systems and communication networks.
• Designing filters and circuits to minimize distortion.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 1: \(\mathrm{THD} = \sqrt{\frac{1}{1+\mathrm{DF}^{2}}}\)

This formula is incorrect. The relationship between DF and THD does not support this formulation. Substituting \(V_{\text{harmonics}} = \mathrm{THD} \cdot V_1\) and \(V_{\text{total}} = V_1 \sqrt{1 + \mathrm{THD}^2}\) into the definition of DF demonstrates that Option 1 does not align with the derived formula.

Option 3: \(\mathrm{DF} = \sqrt{\frac{1}{1-\mathrm{THD}^{2}}}\)

This formula is invalid because it implies a subtraction of \(\mathrm{THD}^2\), which can yield nonsensical or negative values when \(\mathrm{THD} > 1\). The correct formula involves addition (\(1 + \mathrm{THD}^2\)) in the denominator.

Option 4: \(\mathrm{THD} = \sqrt{\frac{1}{1-\mathrm{DF}^{2}}}\)

Similar to Option 3, this formula is incorrect due to the subtraction term (\(1 - \mathrm{DF}^2\)) in the denominator. The derived relationship between DF and THD involves addition, not subtraction.

Conclusion:

The correct formula, \(\mathrm{DF} = \sqrt{\frac{1}{1+\mathrm{THD}^{2}}}\), accurately describes the relationship between distortion factor and total harmonic distortion. This formula is essential in applications where understanding and minimizing waveform distortion is critical, such as in power systems, audio engineering, and signal processing. The incorrect options fail to align with the derived mathematical relationship and can lead to erroneous interpretations if applied.

Explanation:

There are three modes of operation in a SCR. 

1.) Forward conduction mode: In this mode, the anode is connected to the +ve terminal of the battery, and the cathode is connected to a -ve terminal of the battery. A gate signal is applied at the gate terminal, hence a positive current flows from the anode to the cathode.

2.) Forward blocking mode: Anode is connected to the +ve terminal of the battery and the cathode is connected to a -ve terminal of the battery but the gate signal is not applied at the gate terminal, hence a forward leakage current flows from the anode to cathode.

3.) Reverse blocking mode:  In this mode, the anode is connected to a -ve terminal of the battery, and the cathode is connected to the +ve terminal of the battery, hence a reverse leakage current flows from the cathode to the anode.

Explanation:

A SCR conducts when both the below conditions are satisfied.

• When SCR is in forward biased condition i.e. the anode is connected to +ve terminalof battery and the cathode is connected to negative terminal of the battery.
• A positive current flows through the gate terminal of the SCR.

​To turn OFF a conducting SCR properly, the following conditions must be satisfied:

• The anode or forward current of SCR must be reduced to zero or below the level of holding current.
• A sufficient reverse voltage must be applied across the SCR to regain its forward blocking state.

Explanation:

A bidirectional switch is an active switch that has the ability to flow the current in both directions (i.e. from anode to cathode and vice-versa).

SCR allows the current to flow only in one direction from the anode to the cathode.

Hence, it is a unilateral switch.

To turn off the SCR anode current should go less than holding current

⇒ V = 4 × 10^-3 × 4 × 10³

⇒ V = 16 V

for 180° conduction angle α = 0 °

\(\begin{array}{l} {I_{avg}} = \frac{1}{{2\pi }}\mathop \smallint \limits_\alpha ^\pi {I_m}sin\theta\ d\theta = \frac{{{I_m}}}{{2\pi }}\left( {1 + cos\alpha } \right)\\ = \frac{{{I_m}}}{\pi }\\ {I_{rms}} = {\left[ {\frac{1}{{2\pi }}\mathop \smallint \limits_\alpha ^\pi I_m^2{{\sin }^2}\theta\ d\theta } \right]^{\frac{1}{2}}}\\ = \frac{{{I_m}}}{2} \end{array}\)

Form factor \(= \frac{{{I_{rms}}}}{{{I_{avg}}}} = \frac{{\frac{{{I_m}}}{2}}}{{\frac{{{I_m}}}{\pi }}} = \frac{\pi }{2}\)

Current in the circuit is written as following

\(i\left( t \right) = \frac{{{V_s}}}{R}\left( {1 - {e^{ - t\frac{R}{L}}}} \right)\)

\(i\left( t \right) = \frac{{120}}{{20}}\left( {1 - {e^{ - t\frac{{20}}{{0.5}}}}} \right) = 6\;\left( {1-{e^{ - 40t}}} \right)\)

at t = 60 μs

\(i\left( {t = 60\mu s} \right) = \left( {1 - {e^{ - 40 \times 60 \times {{10}^{ - 6}}}}} \right) = 14.38\;mA\)

The resistance R is connected in parallel with circuit increases the current through SCR. SCR takes 14.38 mA current when firing pulse of width 60 μS ends. To latch the SCR, 60 mA current should be passed through it. Hence additional 45.62 mA current can be passed through R as shown in figure.

\(\begin{array}{l} {V_s} = 45.62 \times {10^{ - 3}} \times R\\ \Rightarrow R = \frac{{120}}{{45.62 \times {{10}^{ - 3}}}} = 2.63\;k{\rm{\Omega }} \end{array}\)

Latching current is the minimum value of anode current which it must attain during turn – ON process to maintain conduction when gate signal is removed.

Holding current is the minimum value of anode current below which it must fall for turning – OFF the thyristor.