Form Factor:

• The ratio of the root means square value to the average value of an alternating quantity (current or voltage) is called Form Factor.
• The average of all the instantaneous values of current and voltage over one complete cycle is known as the average value of the alternating quantities.

Mathematically, it is expressed as:

Correct Answer: Start drawing active power from the bus bar and function as a synchronous motor, maintaining its original direction of rotation

When a synchronous generator operating in parallel with an infinite bus bar loses its prime mover's mechanical input, the following happens:

• The machine does not stop immediately because it is still electrically connected to the bus bar.
• Without mechanical input, the machine's torque angle (power angle) reverses from positive to negative.
• The machine starts drawing active power from the bus bar.
• It begins to function as a synchronous motor.
• The machine maintains its original direction of rotation and synchronous speed.

The other options are incorrect because:

• The machine does not cease rotation immediately because the electrical connection with the bus bar keeps it running at synchronous speed.
• It does not continue to operate as a generator because there is no mechanical input to convert into electrical energy.
• Its speed does not gradually decrease because it remains locked at synchronous speed due to the magnetic coupling with the infinite bus bar.

This phenomenon is known as motoring of the generator, and in practice, reverse power relays are used to detect this condition and disconnect the machine from the bus bar to prevent damage to the prime mover.

Correct Answer: Synchronous motors

Synchronous motors are designed to operate at synchronous speed and typically require an external DC excitation for their field winding. Important points about them:

• Synchronous motors run at synchronous speed (Ns = 120f/P) which remains constant regardless of the load.
• Their rotor is excited by an external DC source which produces the magnetic field.
• They are used for constant speed applications and power factor correction.
• They are not self-starting and require special starting mechanisms.

The other options are incorrect because:

• Three-phase induction motors — They run at a speed less than synchronous speed (with slip) and do not require external DC excitation. They work on the principle of electromagnetic induction.
• DC series motors — They run on DC supply and do not require separate field excitation. The field winding is connected in series with the armature.
• Universal motors — They can run on both AC and DC supply and do not require external DC excitation. They are essentially series-wound motors.

Therefore, synchronous motors is the correct answer as they are the only motors that operate exactly at synchronous speed and require external DC excitation for their field winding.

Correct Answer: Feeler gauge

A feeler gauge is the most appropriate instrument for measuring the air gap between the rotor and stator of a starter motor. Important points about it:

• A feeler gauge is a set of thin metal blades of varying thicknesses.
• It is specifically designed for measuring narrow and small clearances.
• It is the most accurate tool for measuring small gaps like 0.40 mm to 0.60 mm.
• It can be directly inserted into the narrow space between the rotor and stator.
• The technician can use different blades to check if the gap falls within the specified range.

The other options are incorrect because:

• Vernier caliper — It is useful for measuring external and internal dimensions but cannot be inserted into narrow air gaps between rotor and stator.
• Taper gauge — It is used for measuring tapered holes and slots, not flat narrow clearances.
• Dial caliper — It is also not suitable for measuring narrow clearances in confined spaces like the gap between rotor and stator.

Therefore, feeler gauge is the correct answer as it is specifically designed for measuring small clearances and gaps in tight spaces, making it the ideal tool for verifying the air gap in a starter motor.

Correct Answer: 0.5

Solution:

Given:

• Characteristic impedance (Z₀) = 75 Ω
• Load impedance (Z_L) = 225 Ω

Formula for Reflection Coefficient (Γ):

Γ = (Z_L - Z₀) / (Z_L + Z₀)

Step 1: Substitute the values

Γ = (225 - 75) / (225 + 75)

Γ = 150 / 300

Γ = 0.5

Therefore, the reflection coefficient is 0.5.

Correct Answer: 1, 3 only

Solution:

For direct coupling, both machines must run at the same synchronous speed.

Step 1: Find the speed of the 8-pole, 50 Hz alternator

Synchronous speed (Ns) = 120f / P

Ns = (120 × 50) / 8

Ns = 6000 / 8

Ns = 750 rpm

Step 2: Check the speed of each synchronous motor

Motor 1: 16 poles, 100 Hz Ns = (120 × 100) / 16 = 12000 / 16 = 750 rpm ✓

Motor 2: 10 poles, 60 Hz Ns = (120 × 60) / 10 = 7200 / 10 = 720 rpm ❌

720 ≠ 750, so this motor cannot be directly coupled.

Motor 3: 4 poles, 25 Hz Ns = (120 × 25) / 4 = 3000 / 4 = 750 rpm ✓

Result:

• Motor 1 → 750 rpm ✓ (matches)
• Motor 2 → 720 rpm ❌ (does not match)
• Motor 3 → 750 rpm ✓ (matches)

Therefore, the correct answer is 1, 3 only. Only Motor 1 and Motor 3 have a synchronous speed of 750 rpm which is equal to the alternator's speed, so only these two can be directly coupled to the alternator.

Correct Answer: The variation of power demand over a 24-hour cycle

A daily load curve directly represents the variation of power demand over a 24-hour cycle. Important points about it:

• In a daily load curve, the X-axis represents time (24 hours) and the Y-axis represents load (MW or kW).
• It shows how the power demand changes at different times of the day.
• It helps identify the peak demand (maximum demand) and minimum demand during the day.
• It is useful for efficient operation and planning of the power generating station.

The other options are incorrect because:

• Annual peak demand of the station — This is obtained from the annual load curve, not the daily load curve.
• Average power consumed by a single customer — The daily load curve shows the total demand of the entire station, not of an individual customer.
• Total number of units generated in a year — This is obtained from annual data, not from a daily load curve.

The daily load curve is an essential tool for power station engineers as it helps in deciding the number of generating units to operate at different times, scheduling maintenance, and optimizing fuel consumption based on the varying demand throughout the day.

Hydroelectric Power Plant Components Explained

This question asks us to identify which component from the given options is typically *not* part of a hydroelectric power plant. Let's examine each component:

Understanding Hydroelectric Power Plants

A hydroelectric power plant generates electricity using the energy of moving water. Water stored at a height (potential energy) is released and flows through pipes to turn turbines, which then drive generators.

Analyzing the Options

• Surge Tank: This is a vital component in many hydroelectric power systems. It's essentially a large vertical chamber connected to the pipeline (penstock). Its primary function is to absorb pressure fluctuations, known as water hammer, which can occur when the flow of water through the penstock changes suddenly (e.g., when the turbine load is adjusted). By providing a space for water to surge into or out of, the surge tank protects the penstock from excessive stress. Therefore, a surge tank is found in hydroelectric power plants.
• Boiler: A boiler is a closed vessel used to heat water and convert it into steam under pressure. This steam is then used to drive turbines in thermal power plants, such as coal-fired, natural gas, or nuclear power plants. Hydroelectric power plants utilize the kinetic and potential energy of water, not steam generated from heating water. Thus, a boiler is not a component of a hydroelectric power plant.
• Penstock: The penstock is a large, high-pressure pipe that carries water from the intake or reservoir directly to the turbine runner. It's a crucial conduit for channeling the water's energy to the generating machinery. Therefore, a penstock is found in hydroelectric power plants.
• Spillway: A spillway is a safety feature of dams, including those used for hydroelectric power generation. It is designed to release excess water from the reservoir, typically during periods of high rainfall or snowmelt, preventing the water level from rising dangerously high and potentially overtopping or damaging the dam structure. Therefore, a spillway is typically found in hydroelectric power plants.

Conclusion on Missing Component

Based on the functions of each component, the boiler is the only item listed that is characteristic of thermal power generation, not hydroelectric power generation. Hydroelectric plants use the force of water, while thermal plants use steam (often produced by boilers) to generate power.

Correct Answer: 271.25 V

Solution:

Given:

• Load power (P) = 10 kW = 10,000 W
• Terminal voltage (V) = 250 V
• Armature resistance (Ra) = 0.5 Ω
• Field resistance (Rf) = 100 Ω

Step 1: Find Load Current (IL)

IL = P / V

IL = 10,000 / 250

IL = 40 A

Step 2: Find Field Current (If)

If = V / Rf

If = 250 / 100

If = 2.5 A

Step 3: Find Armature Current (Ia)

In a shunt generator:

Ia = IL + If

Ia = 40 + 2.5

Ia = 42.5 A

Step 4: Find Generated EMF (Eg)

Eg = V + Ia × Ra

Eg = 250 + 42.5 × 0.5

Eg = 250 + 21.25

Eg = 271.25 V

Therefore, the generated EMF is 271.25 V.

Correct Answer: 

Solution:

The common base DC current gain (α_dc) for a bipolar junction transistor is defined as the ratio of the DC collector current to the DC emitter current.

Formula:

α_dc = I_C / I_E

Important points about α_dc:

• α_dc is always less than 1 (typically 0.95 to 0.99) because the collector current is always slightly less than the emitter current.
• The relationship between currents is: I_E = I_C + I_B
• α_dc represents how much of the emitter current reaches the collector in common base configuration.

The other options are incorrect because:

• I_E / I_B — This is not a standard transistor parameter.
• I_C / I_B — This is the common emitter DC current gain (β_dc), not common base.
• I_E / I_C — This is the inverse of α_dc.

Therefore, the correct equation for common base DC current gain is α_dc = I_C / I_E.