Series RLC circuit:

Differentiating the above equation with respect to t,

By applying the Laplace transform,

Roots

Consider

Resonant frequency

α is the Neper frequency

ω_d is the damped natural frequency.

Parallel RLC circuit:

Differentiating the above equation with respect to t,

Consider

s = α ± jβ

Under the static condition, the electric field inside the solid perfect conductor is zero in electrostatic equilibrium even if:

• it is isolated
• it is charged
• it is present in the external electrostatic field

Now, it is known that a perfect solid conductor is an equipotential body. The potential inside the conductor is the same as the potential at the surface

Since the surface of the solid conductor is an equipotential surface hence the electric field will be perpendicular or in other words normal to the perfectly solid conductor surface.

Absolute Error: The deviation of the measured value from the true value (or) actual value is called error.

Absolute error (E) = A_m – A_t

A_m = Measured value

A_t = True value

Relative Static Error: The ratio of absolute error to the true value is called relative static error.

Limiting Error:

The maximum allowable error in the measurement is specified in terms of true value, is known as limiting error. It will give a range of errors. It is always with respect to true value, so it is a variable error.

Guaranteed Accuracy Error:

The allowable error in measurement is specified in terms of full-scale value is known as a guaranteed accuracy error. It is a variable error seen by the instrument since it is with respect to full-scale value.

Concept:

Resonant frequency for a series RLC circuit is given by:

Bandwidth for a series RLC circuit is given by:

Also, the quality factor is given by:

Calculations:

Given that, R = 10 Ω, L = 25 mH, C = 100 μF

For the given RLC network, the resonant frequency will be:

Qulaity factor, Q = 632.45/400 = 1.58

Pulse Signal:

• To reduce gate power dissipation, SCR firing circuits generate a single pulse or a train of pulses instead of a continuous DC gate signal.
• This allows precise control of the point at which the SCR is fired.
• In addition, it is easy to provide electrical isolation between the SCR and the gate trigger circuit.
• Electrical isolation by means of a pulse transformer or optical coupler is important if several SCR's are gated from the same source.
• Isolation also reduces unwanted signals such as transient noise signals that could inadvertently trigger a sensitive SCR.
• Since in a pulse transformer induced emf is proportional to the frequency, therefore a high frequency train pulse is used to reduce the core size.
• Higher frequencies allow the reducing component size.

Concept:

• When resistors are connected in series, the total resistance is the sum of the individual resistances.

(R_eq )_series = R₁ + R₂ + ………… + R_n

Where, n = 1,2,3 …….

• When resistors are connected in parallel, the total resistance is less than the least resistance connected in series.

Calculation:

By re-drawing given circuit diagram, we get

R_AB = 1 + 0.8 + 1.2

R_AB = 3 Ω

• In ac drives, stable operating point is when load torque is equal to electromagnetic torque
• Criteria for the steady state stability is for a decrease in the speed the motor torque must exceeds the load torque and for increase in speed the motor torque must be less than the load torque.
• To check the stability at an operating point of the motor, if an increase in speed brings greater increase in load torque than the motor torque, the speed will tend to decrease and return to its original value, so operating point will be a stable point else operating point will be an unstable point.

The piezoelectric crystal is used for transmitting as well as receiving acoustic energy in an ultrasonic flow meter.

Ultrasonic Flowmeter:

• Basically, an ultrasonic flowmeter consists of two piezoelectric crystals in liquid or gas separated by a distance d.
• One of the crystal act as a transmitter (T) and other act as a receiver (R) as shown.

• The transmitter emits an ultrasonic pulse which received at the receiver a time Δt later.

This transmitted time (Δt) is given as,

Where, C is the velocity of sound propagation in a given medium and V is the flow velocity.

• By means of this principle, an ultrasonic flowmeter works.
• It has no moving part and allows bidirectionally flow.
• It has linear relation between input and output.

Total harmonic distortion:

• It is a common measurement of the level of harmonic distortion present in power systems.
• THD can be related to either current harmonics or voltage harmonics.
• It is defined as the ratio of r.m.s value of all the harmonic components to the r.m.s value of the fundamental component.
• Mathematically, it can be represented as

Where,

V_or = Total rms value

V­₀₁ = Fundamental rms value

Distortion factor (DF): It is the ratio of the fundamental component to r.m.s value of the waveform.

Distortion factor (DF) and total harmonic distortion (THD) are related as

Full scale reading = 25 A

Guaranteed accuracy error = 1% of full-scale reading = 0.01 × 25 = 0.25 A

Measured value = 5 A

Limiting error

Important Point

Absolute Error:
The deviation of the measured value from the true value (or) actual value is called error.

Absolute error (E) = A_m – A_t

A_m = Measured value

A_t = True value

Relative Static Error:
The ratio of absolute error to the true value is called relative static error.

Limiting Error:
The maximum allowable error in the measurement is specified in terms of true value, is known as limiting error. It will give a range of errors. It is always with respect to the true value, so it is a variable error.

Guaranteed Accuracy Error:
The allowable error in measurement is specified in terms of full-scale value is known as a guaranteed accuracy error. It is a constant error seen by the instrument since it is with respect to full-scale value.

Multi stack variable reluctance stepper motor:

• Multi stack variable stepper motors are used for getting smaller step sizes usually in the range of 2 to 15°.
• The most commonly used multi-stack variable reluctance motor is the three-stack reluctance motor. A multi-stack motor may employ as many as seven stacks.
• An m-stack motor can be viewed as consisting of m identical single stack variable reluctance motors with their rotors mounted on a common shaft.
• The stators and rotors have the same number of poles (or teeth), and therefore, the same pole pitch.
• While the stator poles (teeth) in all m stacks are aligned, the rotor poles are shifted by 1/m of the pole pitch from one another.
• All the stator pole windings in a given stack are excited simultaneously.
• Since all the stator pole windings in a given stack are excited simultaneously, the stator winding of each stack forms one phase. Thus the motor has the same number of phases as the number of stacks.

​

Figure: Cross-section of three stack variable reluctance motor

Important point:

In each stack, stators and rotors have 12 poles. While the stator poles in the three stacks are aligned, the rotor poles are offset from each other by one-third of the pole pitch or 10°.

Let N be the number of rotor poles (or teeth) and m is the number of stacks or phases. Then

Pole pitch = 360° / N

Step angle = 360° / (m × N)

Concept:

1. Every branch of a root locus diagram starts at a pole (K = 0) and terminates at a zero (K = ∞) of the open-loop transfer function.

2. Root locus diagram is symmetrical with respect to the real axis.

3. Number of branches of the root locus diagram are:

N = P if P ≥ Z

= Z, if P ≤ Z

4. Number of asymptotes in a root locus diagram = |P – Z|

5. Centroid: It is the intersection of the asymptotes and always lies on the real axis. It is denoted by σ.

ΣPi is the sum of real parts of finite poles of G(s)H(s)

ΣZi is the sum of real parts of finite zeros of G(s)H(s)

6. Angle of asymptotes:

l = 0, 1, 2, … |P – Z| – 1

7. On the real axis to the right side of any section, if the sum of the total number of poles and zeros are odd, the root locus diagram exists in that section.

8. Break in/away points: These exist when there are multiple roots on the root locus diagram.

At the breakpoints gain K is either maximum and/or minimum.

So, the roots of are the break points.

Application:

The loop transfer function of a system is given by:

Number of open loop poles = 3

Number of open loop zeros = 0

Number of Asymptotes = |3 – 0| = 3

Centroid,

Centroid

Ratio error in current transformer:

• In the current transformer, the primary current Ip should be exactly equal to the secondary current multiplied by turns ratio, i.e. KTIs.
• But there is a difference between primary current Ip should be exactly equal to the secondary current multiplied by the turns ratio.
• This difference is contributed by the core excitation or magnetizing component of no-load current.
• The error in the current transformer introduced due to this difference is called current error or ratio error.

The actual ratio of transformation varies with operating conditions and the error in secondary voltage is defined as

Percentage ratio error

Kn is the nominal ratio

R is the actual ratio

It can be reduced by secondary turns compensation i.e. slightly decreasing the secondary turns.

Phase angle error:

In an ideal voltage transformer, there should not be any phase difference between the primary voltage and the secondary voltage reversed. However, in an actual transformer, there exists a phase difference between Vo­ and V­s reversed.

The phase angle is taken as +ve when secondary voltage reversed leads the primary voltage.

The angle is -ve when the secondary voltage reversed lags the primary voltage.

It can be reduced by keeping the primary and secondary windings are wound as closely as possible.

Concept:

According to Mason’s gain formula, the transfer function is given by

Where,

n = no of forward paths

Mk = kth forward path gain

Δk = the value of Δ which is not touching the kth forward path

Δ = 1 – (sum of the loop gains) + (sum of the gain product of two non-touching loops) – (sum of the gain product of three non-touching loops)

Application:

Forward path = X₁ → X₂ → X₃ → X₄ = abc

Feedback path = X₂ → X₃ → X₂ = bd

Δ = 1 – bd

By using Mason’s gain formula,

Total gain,

Concept:

• Astable Multivibrators are free-running oscillators that oscillate between two states continuously producing two square wave output waveforms.
• These both states are not stable as it changes from one state to the other all the time.
• As the Multivibrator keeps on switching, these states are known as quasi-stable or half-stable states.

Important Point

• A Monostable multivibrator has a stable state and a quasi-stable state. This has a trigger input to one transistor. So, one transistor changes its state automatically, while the other one needs a trigger input to change its state.
• A Bistable multivibrator has both the two states stable. It requires two trigger pulses to be applied to change the states. Until the trigger input is given, this multivibrator cannot change its state.

Laws of Boolean Algebra:

Application:

f(A, B) = ∑ m(0, 1, 2, 3)

= A̅ B̅ + A̅ B + A B̅ + AB

= A̅ ( B + B̅) + A (B̅ + B)

= A̅ + A = 1

Concept:

The power triangle is shown below.

P = Active power (or) Real power in W = V_rI_r cos ϕ = (I_r)²R = S cos ϕ

Q = Reactive power in VAR = V_rI_r sin ϕ

S = Apparent power in VA = V_rI_r = (I_r)²Z

Where,

V_r and I_r is the RMS value of voltage and current.

R is resistance Ω.

Z is impedance in Ω.

S = P + jQ

ϕ is the phase difference between the voltage and current

Power factor

Calculation:

Given, Z = (4 - j3) Ω

∴

Hence, Power factor will be,

Given, i = 5cos (100πt + 100) A

Where, I_m = 5 A

∴ RMS Value of current, (I_r) = 5/√2 A

From above concept,

P = S cos ϕ = (I_r)²Z cos ϕ

∴

The armature MMF of a distributed armature winding of a dc machine is triangular in shape as shown in fig.

In a D.C. machine, the armature M.M.F. wave has its maximum value at fixed points between the main poles.

By applying KVL in the outer loop as shown, we get

1 – 1 – (I × 1) = 0

⇒ I = 0

V’ = I × 1 = 0 V

Now, the circuit can be modified as shown below

Now, by applying nodal analysis at node A

⇒ V_A = 1.5 V

Voltage across current source = 1.5 V

Power developed by current source = VI = 1.5 × 2 = 3 W

• Meaning of Warrior: A brave or experienced soldier or fighter.
• Meaning of Sailor: a person who goes sailing as a sport or recreation
• Meaning of Pirate: a person who attacks and robs ships at sea
• Meaning of Spy: a person employed by a government or other organization to secretly obtain information on an enemy or competitor

Use structure “subject + auxiliary + past participle ”
As per the given above sentence is given in Passive Voice.
You have been warned.
Therefore , required answer will be option A .

Setup Options in Page Setup Dialog Box:
The page setup dialog box allows users to customize various settings for printing a document. Here are the setup options that can be set in the page setup dialog box:
1. Orientation: Users can specify whether they want the document to be printed in portrait (vertical) or landscape (horizontal) orientation.
2. Margin settings: Users can adjust the margins of the document, controlling the amount of white space around the content.
3. Paper size: Users can select the size of the paper on which they want to print the document, such as A4, Letter, Legal, etc.
4. Headers and footers: Users can choose to include headers and footers on the printed document, which can contain page numbers, document titles, dates, and other information.
5. Scaling: Users can adjust the scaling of the document, allowing them to print the content at a smaller or larger size.
6. Print quality: Users can select the print quality, choosing between options like draft, normal, or high quality.
7. Page order: Users can specify the order in which the pages should be printed, such as from top to bottom or from left to right.
8. Row and column titles: Users can choose to repeat row and column titles on each printed page, ensuring that the headers are visible on every page.
However, there is one setup option that cannot be set in the page setup dialog box:
- Printer selection: The page setup dialog box does not provide an option to select a specific printer. Printer selection is usually done through the print dialog box, where users can choose the printer they want to use.
Therefore, option A: "Printer selection" cannot be set in the page setup dialog box.

The correct answer is Used for creating a chart from the selected cell.

Key Points

• The function of F11 in the Excel sheet is that it is used for creating a chart from the selected cell.
  • It creates a chart of the data in the current range in a separate Chart sheet.
  • Alt+F1 shortcut creates a default chart as a chart object embedded in the current worksheet.

Additional Information

•  Some important shortcuts used in MS Excel
  • F1 Opens Excel Help
  • F2 Edit contents of an excel
  • F3 Paste Named Range or Named List
  • F4 Toggles between cell references – Absolute, Relative, and Mixed Reference
  • F5 Displays the "Go To" dialog box
  • F6 Switch between the panes of an excel workbook if you have a split window
  • F7 Opens the "Spelling" option in excel using which you can check the spellings in your workbook
  • F8 Enables and disables the "Extend Mode" selection in excel.
  • F9 Recalculates the output of all formulas in your excel workbook.
  • F10 Displays the keyboard shortcut for the excel ribbon also known as excel tips
  • F12 Opens the "Save As" dialog box like the "Alt + F2" keys

The correct answer is VSTACK.

Key Points

• MS Excel allows you to combine two or more ranges of cells or arrays in two ways i.e., vertically or horizontally.
• VSTACK is a function that combines two or more arrays vertically. Hence option 2 is correct.
  • Its syntax is VSTACK(array1, [array2],...).

Additional Information

• HSTACK is another function that works similarly to the VSTACK function, but the former function combines the range of the cells horizontally.
  • Its syntax is HSTACK(array1, [array2],..).
• Excel provides SORT() function to arrange the values according to the given requirements.

Process Control Block (PCB)

• Process number: The PCB contains the unique identifier or process number assigned to the process by the operating system.


• List of open files: The PCB includes a list of files that the process has currently opened. This list helps the operating system keep track of the files being accessed by the process.


• Memory limits: The PCB stores information about the memory limits for the process, including the start and end addresses of the process's memory allocation.

Therefore, the correct answer is All of these, as all the given options are contained in the process control block.

Term used when you press and hold the left mouse key and move the mouse around the slide:

• Dragging: This is the correct term used when you press and hold the left mouse key and move the mouse around the slide. It refers to the action of moving an object or selecting multiple objects by holding down the mouse button and moving the cursor.


• Highlighting: This term is not applicable in this context. Highlighting usually refers to the action of selecting text or a portion of text by changing its background color.


• Selecting: This term is also not specifically used to describe the action of pressing and holding the left mouse key and moving the mouse around the slide. Selecting typically refers to choosing or picking something from a list or group of items.


• Both (b) and (c): This option is incorrect because the correct term for pressing and holding the left mouse key and moving the mouse around the slide is only dragging. The term "selecting" is not accurate in this context.

Therefore, the correct term used when you press and hold the left mouse key and move the mouse around the slide is dragging.

Explanation:
To insert a new line in the same cell in Excel, you can use the shortcut Alt + Enter. Here is a detailed explanation of why this is the correct answer:
1. Enter:
- The Enter key is used to move to the next cell in Excel, not to insert a new line within the same cell.
2. Alt + Enter:
- This shortcut is used to insert a new line within the same cell in Excel.
- It allows you to create multiple lines of text within a single cell, which is useful for organizing information or creating lists.
3. Ctrl + Enter:
- The Ctrl + Enter shortcut is used to fill the selected cells with the same data.
- It is not used to insert a new line within a cell.
4. Shift + Enter:
- The Shift + Enter shortcut is not used to insert a new line within a cell in Excel.
- It is used in other applications, such as Microsoft Word, to create a line break without creating a new paragraph.
In conclusion, the correct shortcut to insert a new line in the same cell in Excel is Alt + Enter. This allows you to create multiple lines of text within a single cell for better organization and presentation of data.

First and fouth letters are interchanged while second and third letters are interchanged.

Checking Statement I:

Since there is no information about Monika's rank. Therefore, Rahul's rank cannot be determined.

Clearly, Statement I alone is not sufficient to answer the question.

Checking Statement II:

Aditi's rank and Monika's rank is not given. Therefore, Rahul's rank cannot be determined.

Clearly, Statement II alone is not sufficient to answer the question.

Checking Both statement I and II:

Ranks are not known for any of them. Thus, Rahul's rank cannot be found.

Clearly, Both statements I and II  is not sufficient to answer the question.

Hence, Option D is correct.

Carpenter, Plumber, Electrician and Blacksmith are in same working category.