All questions of Practice and Mock Tests for Electrical Engineering (EE) Exam

25 Hz.

Explanation:

The synchronous speed of a 6 pole induction motor operated on 50 Hz supply is:

Ns = (120 x f) / P = (120 x 50) / 6 = 1000 rpm

Since the motor is driven at 1500 rpm in the opposite direction, the actual speed of the rotor is:

N = Ns - Nr = 1000 - 1500 = -500 rpm

The slip of the motor is given by:

s = (Ns - N) / Ns = (1000 + 500) / 1000 = 1.5

The frequency generated by the slip ring is given by:

f = s x fsupply = 1.5 x 50 = 75 Hz

However, since the motor is operated in the opposite direction, the frequency generated is:

f = fsupply - fslip = 50 - 75 = -25 Hz

Since negative frequency is not physically possible, we take the absolute value:

|f| = 25 Hz

Therefore, the supply frequency generated by the slip ring motor is 25 Hz.

Option b is correct
32=(25+20+15)-(15+5+(x+3))+3
32=60-23-x+3
32=40-x
x=8

Understanding Per Unit System
In electrical engineering, the per unit system is a method used to normalize system quantities. This allows for easier comparison and calculation across different systems.
Given Data
- Transformer ratings: 220/440 V
- Power rating: 5 kVA
- Leakage reactance (low-tension side): 0.05 Ω
Calculating Base Values
1. Base Voltage on Low-Tension Side (V_base):
- V_base = 220 V
2. Base Power (S_base):
- S_base = 5 kVA = 5000 VA
3. Base Reactance (X_base):
- X_base = V_base^2 / S_base
- X_base = (220 V)² / (5000 VA)
- X_base = 48400 / 5000
- X_base = 9.68 Ω
Calculating Per Unit Leakage Reactance
To find the per unit (pu) leakage reactance:
- Per Unit Reactance (X_pu):
- X_pu = Actual Reactance / Base Reactance
- X_pu = 0.05 Ω / 9.68 Ω
- X_pu = 0.005171
Rounding to Four Decimal Places
- Rounding 0.005171 to four decimal places gives:
- X_pu = 0.0051
Conclusion
The per unit leakage reactance of the transformer is 0.0051. This normalized value simplifies analysis in power systems, allowing engineers to easily compare different transformers and their reactances.

Maximum frequency of input in dual slop A/D converter is given as

Understanding the Given Differential Equation
The equation provided is:
y log y dx + (x – log y) dy = 0
This is a first-order differential equation that can be analyzed for an integrating factor.
Identifying the Components
To find the integrating factor, we rewrite the equation in the standard form:
M(x, y) = y log y,
N(x, y) = x - log y.
Here, M and N are functions of x and y.
Calculating the Partial Derivatives
Next, we calculate the partial derivatives:
- ∂M/∂y = log y + 1
- ∂N/∂x = 1
We check for exactness:
- If ∂M/∂y ≠ ∂N/∂x, the equation is not exact.
Since log y + 1 ≠ 1, the equation is not exact.
Finding the Integrating Factor
For the equation to become exact, we seek an integrating factor that depends solely on y. The integrating factor is typically of the form µ(y).
The ratio of the differences of the partial derivatives gives us a clue:
µ(y) = (∂N/∂x) / (∂M/∂y - ∂N/∂x)
Substituting the values:
µ(y) = 1 / (log y + 1 - 1) = 1 / log y
Thus, the integrating factor simplifies to:
µ(y) = log y
Conclusion
The integrating factor for the given differential equation is indeed log y, confirming that option 'B' is the correct answer. This factor can be used to multiply the entire equation, making it exact and solvable.

Measurement of Transformer Parameters Using Wattmeters

Open Circuit Test:

- Wattmeter W2 and W3 are not suitable as they have low power factor and high power factor respectively which will not give accurate readings for open circuit test.
- Wattmeter W1 can be used as it can measure up to 250V and 10A, which is suitable for measuring the voltage and current of the high voltage winding of the transformer during open circuit test.
- Wattmeter W4 can also be used as it can measure up to 150V and 5A, which is suitable for measuring the voltage and current of the low voltage winding of the transformer during open circuit test.
- Therefore, the wattmeters used in open circuit test of the transformer will be W1 and W4.

Short Circuit Test:

- Wattmeter W1 is not suitable for short circuit test as it can measure up to 250V and 10A, which is too high for measuring the voltage and current of the low voltage winding of the transformer during short circuit test.
- Wattmeter W4 is also not suitable for short circuit test as it can measure up to 150V and 5A, which is too low for measuring the voltage and current of the high voltage winding of the transformer during short circuit test.
- Wattmeter W2 can be used as it can measure up to 250V and 5A, which is suitable for measuring the voltage and current of the high voltage winding of the transformer during short circuit test.
- Wattmeter W3 can also be used as it can measure up to 150V and 10A, which is suitable for measuring the voltage and current of the low voltage winding of the transformer during short circuit test.
- Therefore, the wattmeters used in short circuit test of the transformer will be W2 and W3.

Conclusion:

- The suitable wattmeters for open circuit test of the transformer are W1 and W4, while the suitable wattmeters for short circuit test of the transformer are W2 and W3.
- Therefore, the correct answer is option D.

From given state table easily form the state diagram in step by step manner as,

Previously the substation was working on 0.9 leading.

The rectification efficiency of a single-phase half-wave controlled rectifier can be calculated using the following formula:

η = (Vdc / Vac) × 100

Where:
η is the rectification efficiency
Vdc is the DC output voltage
Vac is the AC input voltage

In a half-wave controlled rectifier, the output voltage is given by the equation:

Vdc = (2 / π) * Vac * (1 - cos(α))

Where:
α is the delay angle

To calculate the rectification efficiency, we need to substitute the values into the equations and solve for η.

Given:
Delay angle (α) = π/2

1. Calculate the DC output voltage (Vdc):
Vdc = (2 / π) * Vac * (1 - cos(π/2))
= (2 / π) * Vac * (1 - 0)
= (2 / π) * Vac

2. Calculate the rectification efficiency (η):
η = (Vdc / Vac) × 100
= [(2 / π) * Vac / Vac] × 100
= (2 / π) × 100
≈ 20.23%

Therefore, the rectification efficiency of the single-phase half-wave controlled rectifier with a resistive load and a delay angle of π/2 is approximately 20.23%.

Note: The rectification efficiency represents the percentage of AC power converted into DC power. In this case, since we are using a half-wave rectifier, only half of the AC input waveform is utilized, resulting in a lower rectification efficiency compared to full-wave rectifiers. The delay angle determines the point in the AC cycle at which the rectifier starts conducting, and a delay angle of π/2 means the rectifier conducts from the peak of the AC waveform.

Understanding the Argument
The argument presented highlights the extensive seal hunting in Canada, emphasizing the scale of the slaughter and its implications. Among the assumptions made, option 'B' is considered correct.
Key Points Supporting Option 'B'
- Economic Motivation: The argument implies that seal hunting is a significant commercial activity, suggesting that seals serve as a source of income for those involved in the hunt.
- Commercial Quotas: The mention of specific quotas for hunting indicates that the government recognizes the commercial value of seal hunting, reinforcing the idea that it contributes to the economy.
- Government Oversight: The existence of quotas and the regulation of seal hunting imply that the government is actively involved in managing this practice for economic benefit.
Why Other Options are Less Relevant
- Need to Control Population (Option A): While there may be discussions about seal population control, the argument does not explicitly state that there is an excessive number of seals needing removal for ecological reasons.
- Cruelty of the Slaughter (Option C): Although the argument suggests that the slaughter is massive and implies cruelty, it does not make a direct assumption about the inherent cruelty being a primary reason for the hunt.
- Legality of Killings (Option D): The argument mentions exceeded quotas but does not indicate that these excessive killings are punishable by law, making this assumption unsupported.
Conclusion
In summary, option 'B' stands out as it directly relates to the economic aspects of seal hunting, which is a central theme in the argument. The other options lack explicit support or relevance to the core message.

Set A = {2, 3, 4, 5}

Understanding the Statements
To analyze the conclusions, let's break down the statements:
- Statement (i): All airports are tidy.
- Statement (ii): Some departments are neat.
- Statement (iii): Some airports are departments.
Analyzing the Conclusions
Now, let's evaluate each conclusion:
- Conclusion (i): Some departments are tidy.
- Given that all airports are tidy and some airports are departments, it logically follows that some departments must be tidy. Thus, this conclusion is valid.
- Conclusion (ii): Some airports are neat.
- Since some departments are neat and some airports are departments, it can be inferred that at least some airports are neat. Therefore, this conclusion also holds true.
- Conclusion (iii): No neat is airport.
- This conclusion is not supported by the statements. The statements do not provide any basis for assuming that neat departments cannot be airports. Thus, this conclusion does not follow.
Final Evaluation
Considering the evaluations:
- Conclusion (i) is true.
- Conclusion (ii) is true.
- Conclusion (iii) is false.
Therefore, the correct option is (c): (i) and either (ii) or (iii) follow. Since both (i) and (ii) are valid while (iii) is not, option (c) is indeed the right answer.
This logical deduction showcases the importance of carefully analyzing premises to derive valid conclusions.

Number of Triangles in a Heptagon

To find the number of triangles that can be formed by joining the vertices of a heptagon, let's break down the problem step by step.

Step 1: Understanding a Heptagon
A heptagon is a polygon with seven sides and seven vertices. Each vertex can be connected to any other vertex to form a triangle.

Step 2: Counting Triangles
To count the number of triangles, we need to consider the possible combinations of three vertices chosen from the seven available vertices.

Step 3: Applying Combinations
To calculate the number of combinations, we can use the formula for combinations:

C(n, r) = n! / (r!(n-r)!)

Where n is the total number of items, and r is the number of items chosen at a time.

In this case, n = 7 (number of vertices) and r = 3 (number of vertices needed to form a triangle).

C(7, 3) = 7! / (3!(7-3)!)
= 7! / (3!4!)
= (7 * 6 * 5 * 4!) / (3 * 2 * 1 * 4!)
= (7 * 6 * 5) / (3 * 2 * 1)
= 35

Therefore, the number of triangles that can be formed by joining the vertices of a heptagon is 35.

Answer: Option B (35)

Silence refers to 'no speech'. Babble means continuous, and sometimes incoherent speech.

Probability that A and B will contradict each other is that A speaks truth and B lies

Pronoun inconsistency.The pronoun should be ‘their’ instead of ‘his’ as it refers to rainforests.So, option (D) should be corrected.

The sentence implies that the custom authorities seized many items made of ivory.

Current across capacitor

Given data L = 50 mH, C = 0.05 μF

Given circuit is shown below

Understanding Rolle's Theorem
Rolle's Theorem states that if a function is continuous on a closed interval [a, b], differentiable on the open interval (a, b), and f(a) = f(b), then there exists at least one c in (a, b) such that f'(c) = 0.
Function Details
For the given function f(x) = x³ - 6x² + kx + 5:
- Interval: [1, 3]
- c: Given as +1/3
Step 1: Check Continuity and Differentiability
- The function is a polynomial, thus continuous and differentiable everywhere, including the interval [1, 3].
Step 2: Calculate f(1) and f(3)
- f(1):
f(1) = 1³ - 6(1)² + k(1) + 5 = 1 - 6 + k + 5 = k
- f(3):
f(3) = 3³ - 6(3)² + k(3) + 5 = 27 - 54 + 3k + 5 = 3k - 22
Step 3: Set f(1) = f(3)
To satisfy Rolle's theorem:
- k = 3k - 22
Rearranging gives:
- 22 = 2k
- k = 11
Conclusion
Thus, the value of k, satisfying the conditions of Rolle's theorem for the function on the interval [1, 3] is:
- k = 11
This aligns with the correct answer provided.

Given:

• Firing angle, α = 300


• Maximum phase voltage, Vm = 400 V

To find:

• Peak to peak ripple voltage

Concepts Used:

• For a fully controlled natural commutated 3-Φ bridge rectifier, the output voltage V0 can be given as:

V0 = √2Vmcosα

Calculation:

• Given firing angle, α = 300


• Maximum phase voltage, Vm = 400 V


• Using the above formula, we can find the output voltage as:

V0 = √2Vmcosα
= √2 x 400 x cos300
= √2 x 400 x (0.866)
= 400√3 V

Peak to Peak Ripple Voltage:

• For a fully controlled natural commutated 3-Φ bridge rectifier, the peak to peak ripple voltage can be given as:

Vrpp = V0 / √3

Substituting the value of V0, we get:

Vrpp = 400√3 / √3
= 400 V

Answer:

• Peak to peak ripple voltage = 400 V

Synchronous Reactance

The synchronous reactance is an important parameter in the analysis and design of synchronous machines. It represents the opposition offered by the machine to the flow of synchronous current. The synchronous reactance mainly consists of two components - armature leakage reactance and magnetization reactance.

Armature Leakage Reactance

The armature leakage reactance is the reactance due to the leakage flux in the armature winding. When the synchronous machine is in operation, some of the flux produced by the field winding does not link with the armature winding due to leakage. This leakage flux induces an emf in the armature winding, which leads to the flow of armature leakage current. The armature leakage reactance represents the opposition offered by the armature winding to this leakage current.

Magnetization Reactance

The magnetization reactance is the reactance due to the magnetization current required to establish the magnetic field in the machine. When the synchronous machine is excited with a field current, it generates a magnetic field. This magnetic field induces a voltage in the armature winding, which leads to the flow of magnetization current. The magnetization reactance represents the opposition offered by the machine to this magnetization current.

Synchronous Reactance Calculation

The synchronous reactance is the sum of the armature leakage reactance and magnetization reactance. This can be mathematically represented as:

Synchronous Reactance = Armature Leakage Reactance + Magnetization Reactance

This is because both the armature leakage reactance and magnetization reactance contribute to the total opposition offered by the machine to the flow of synchronous current.

Conclusion

In conclusion, the synchronous reactance is equal to the sum of the armature leakage reactance and magnetization reactance. It represents the opposition offered by the synchronous machine to the flow of synchronous current. The armature leakage reactance accounts for the leakage flux in the armature winding, while the magnetization reactance accounts for the magnetization current required to establish the magnetic field. Understanding and accurately calculating the synchronous reactance is essential for the analysis and design of synchronous machines.

Explanation:
It is not wise relying to anybody too much.
Analysis:
The correct preposition to use after the verb "rely" is "on." Therefore, the correct structure of the sentence should be "It is not wise to rely on anybody too much."
Corrected Sentence:
It is not wise to rely on anybody too much.
Therefore, option (c) - to rely on anybody - is the most appropriate substitution for the underlined segment in the given sentence.