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Past Questions
The electric field on equipotential surface is :
A)
Unity
B)
Always perpendicular to the surface
C)
Always parallel to the surface
D)
Zero
An equipotential surface is defined as a surface where the electric potential (V) is constant at every point. The relationship between the electric field (E) and the electric potential is given by the gradient: E = -∇V. Mathematically, the work done (W) in moving a charge (q) along an equipotential surface is W = qΔV. Since ΔV = 0 on an equipotential surface, the work done is zero. Work is also defined as W = ∫ E · dl cos(θ). For the work to be zero for any displacement (dl) along the surface, the cosine of the angle (θ) between the electric field vector and the displacement vector must be zero, meaning θ = 90°. Therefore, the electric field must always be perpendicular to the equipotential surface.
Why other options are incorrect:
- Option (a) Unity: The magnitude of the electric field depends on the charge distribution and distance, not a constant value of 1.
- Option (c) Always parallel: If the field were parallel, there would be a potential difference between points on the surface, contradicting the definition of an equipotential surface.
- Option (d) Zero: The electric field is not necessarily zero; it is simply perpendicular to the surface. A zero field would imply no charge source nearby.
The impurity atoms in semiconductors :
A)
reduce the energy gap
B)
increase the kinetic energy of valence electrons
C)
inject more charge carriers
D)
increase the energy release
The process of adding impurity atoms to an intrinsic (pure) semiconductor is called 'doping'. The primary purpose of doping is to increase the electrical conductivity of the material.
1. **Mechanism**: In an n-type semiconductor, pentavalent impurities (like Phosphorus) are added, which provide extra electrons (negative charge carriers). In a p-type semiconductor, trivalent impurities (like Boron) are added, which create 'holes' (positive charge carriers) by accepting electrons from the valence band.
2. **Effect**: By introducing these impurities, the concentration of free charge carriers (either electrons or holes) is significantly increased compared to the intrinsic state, thereby 'injecting' more carriers into the crystal lattice.
Why other options are incorrect:
- **Option a**: Impurity atoms create new energy levels (donor or acceptor levels) within the existing energy gap, but they do not reduce the fundamental band gap (Eg) of the semiconductor material itself.
- **Option b**: Kinetic energy of electrons is primarily a function of temperature and the electric field applied, not the presence of impurity atoms.
- **Option d**: 'Energy release' is not a standard term describing the effect of doping on the electrical properties of a semiconductor.
What is a semiconductor? How does it differ from conductor and insulator? Write some properties of semiconductors.
The accuracy of moving coil instruments as compare to moving iron instruments is :
A)
high
B)
low
C)
same
D)
reasonable accurate
Permanent Magnet Moving Coil (PMMC) instruments are significantly more accurate than Moving Iron (MI) instruments due to several fundamental design factors:
1. Linear Scale: PMMC instruments have a linear scale because the deflecting torque is directly proportional to the current (Td ∝ I). In contrast, MI instruments have a non-linear (squared) scale (Td ∝ I²), which leads to lower precision, especially at the lower end of the scale.
2. Hysteresis and Eddy Currents: MI instruments use ferromagnetic materials that are subject to hysteresis and eddy current losses, which introduce errors. PMMC instruments use a permanent magnet and a coil, avoiding these specific magnetic losses in the moving part.
3. Sensitivity: PMMC instruments are much more sensitive and can detect very small changes in current compared to MI instruments.
4. External Field Interference: PMMC instruments are typically shielded from stray magnetic fields, whereas MI instruments are more susceptible to external magnetic interference.
Therefore, when comparing the two, the accuracy of moving coil instruments is high.
Regarding Thevenin equivalent, which of the following is not correct?
A)
The voltage source in the Thevenin equivalent circuit is the open circuit voltage of the network when load is disconnected.
B)
The Thevenin equivalent resistance (impedance) is the resistance (impedance) of the network when all voltage sources are short circuited.
C)
Thevenin equivalent resistance is calculated when all voltage sources are open circuited.
D)
Thevenin equivalent is the voltage equivalent of the network.
Thevenin's Theorem states that any linear electrical network with voltage and current sources and resistances can be replaced at its terminals by an equivalent voltage source (Vth) in series with an equivalent resistance (Rth).
Let's analyze the options:
- Option (a) is CORRECT: The Thevenin voltage (Vth) is indeed the open-circuit voltage measured across the load terminals when the load is removed.
- Option (b) is CORRECT: To find the Thevenin resistance (Rth), all independent sources must be deactivated. Deactivating a voltage source means replacing it with its internal resistance, which for an ideal voltage source is a short circuit (0 ohms).
- Option (c) is INCORRECT: This is the opposite of the correct procedure. Voltage sources are short-circuited, not open-circuited, when calculating the equivalent resistance. Current sources are the ones that are open-circuited.
- Option (d) is CORRECT: Thevenin's theorem provides a voltage-source equivalent, whereas Norton's theorem provides a current-source equivalent.
Since the question asks which statement is NOT correct, option (c) is the right answer.
Explain the concept of superconductivity. Also draw the magnetic field Vs Temperature characteristics.
What do you mean by insulating materials? Explain its classification based on temperature.
Suppose that resistors R1 and R2 are connected in parallel to give an equivalent resistor R. If resistors R1 and R2 have tolerance of 1% each, the equivalent resistor R for resistors R1 =300 W and R2 =200 W will have tolerance of :
A)
0.5%
B)
1%
C)
1.2%
D)
2%
To find the tolerance of the equivalent resistance R for two resistors R1 and R2 in parallel, we use the formula for parallel resistance: 1/R = 1/R1 + 1/R2, or R = (R1 * R2) / (R1 + R2).
Given:
- R1 = 300 Ω, Tolerance (dR1/R1) = 1% = 0.01
- R2 = 200 Ω, Tolerance (dR2/R2) = 1% = 0.01
Using the method of partial derivatives for error propagation, the relative error (tolerance) of R is given by:
dR/R = |(∂R/∂R1) * (dR1/R)| + |(∂R/∂R2) * (dR2/R)|
Alternatively, for a product/quotient relationship, we can use the logarithmic differentiation method:
ln(R) = ln(R1) + ln(R2) - ln(R1 + R2)
Taking the differential:
dR/R = dR1/R1 + dR2/R2 - d(R1+R2)/(R1+R2)
Let's calculate the specific weights:
1. dR/R = (R2 / (R1 + R2)) * (dR1/R1) + (R1 / (R1 + R2)) * (dR2/R2)
2. Substitute the values:
dR/R = (200 / (300 + 200)) * (1%) + (300 / (300 + 200)) * (1%)
dR/R = (200 / 500) * 1% + (300 / 500) * 1%
dR/R = 0.4 * 1% + 0.6 * 1%
dR/R = 0.4% + 0.6% = 1%
Therefore, the tolerance of the equivalent resistor R is 1%. This makes sense intuitively: if both components have the same percentage tolerance, the combined parallel (or series) resistance will also maintain that same percentage tolerance.
Explain the difference in conduction properties of conductors, semiconductors and insulators on the basis of energy band diagram?
What is a thermocouple? Briefly explain the thermoelectric laws.
Fields are said to be circularly polarized if their magnitudes are :
A)
Equal and they are in phase
B)
Equal and they differ in phase by ± 90°
C)
Unequal and they differ in phase by ± 90°
D)
Unequal and they are in phase
Circular polarization occurs when a wave is composed of two orthogonal linear components (e.g., along the x and y axes) that satisfy two specific conditions: 1) The magnitudes of the two components must be equal. 2) The phase difference between the two components must be exactly 90 degrees (π/2 radians) or 270 degrees (-90 degrees). Under these conditions, the resultant electric field vector maintains a constant magnitude but rotates in a circle as the wave propagates.
Analysis of other options:
- Option (a): If magnitudes are equal and they are in phase, the result is a linearly polarized wave oriented at 45 degrees.
- Option (c): If magnitudes are unequal but the phase difference is 90°, the result is elliptical polarization.
- Option (d): If magnitudes are unequal and they are in phase, the result is a linearly polarized wave at an angle determined by the ratio of the magnitudes.
A 0.2 H inductor with an initial current of 4 A is in parallel with a resistor of 100 W. The current at 0.8ms is :
A)
4e^-0.4 A
B)
4e^-16x10^-6 A
C)
4e^-0.4x10^-3 A
D)
4e^-16x10^-3 A
1. **Identify the Circuit Type**: This is a source-free RL circuit where an inductor (L) is in parallel with a resistor (R). In such a configuration, the inductor discharges its stored energy through the resistor.
2. **Given Parameters**:
- Inductance (L) = 0.2 H
- Resistance (R) = 100 Ω (Note: The question says '100 W', which is a typo for 100 Ω)
- Initial Current (I₀) = 4 A
- Time (t) = 0.8 ms = 0.8 × 10⁻³ s
3. **Formula for Current Decay**: The current through an inductor in an RL circuit decays exponentially according to the formula:
i(t) = I₀ * e^(-t / τ)
where τ (time constant) = L / R
4. **Calculate the Time Constant (τ)**:
τ = L / R = 0.2 / 100 = 0.002 s = 2 ms
5. **Calculate the Current at t = 0.8 ms**:
i(0.8ms) = 4 * e^(-0.8 × 10⁻³ / 0.002)
i(0.8ms) = 4 * e^(-0.4)
6. **Conclusion**: The current at 0.8 ms is 4e⁻⁰.⁴ A. Comparing this to the options, option (a) matches exactly. Options (b), (c), and (d) result from incorrect calculations of the exponent or incorrect handling of the time units.
In a conductor the static electric field is :
A)
unity
B)
always perpendicular to the surface
C)
always parallel to the surface
D)
zero
In electrostatics, a conductor is a material that allows free movement of electrons. When a conductor is placed in an external electric field or given a net charge, the free electrons redistribute themselves almost instantaneously. If there were a non-zero electric field inside the conductor, the free charges would experience a force (F = qE) and move. This movement continues until the internal electric field created by the redistributed charges exactly cancels out the external electric field. Therefore, in a state of electrostatic equilibrium, the net electric field inside the bulk of a conductor is always zero.
Analysis of other options:
- Option (a) 'unity' is incorrect as there is no physical basis for the field to be exactly 1 V/m.
- Option (b) 'always perpendicular to the surface' describes the electric field at the SURFACE of the conductor, not 'in' (inside) the conductor.
- Option (c) 'always parallel to the surface' is incorrect because any parallel component of the field would cause charges to move along the surface until that component is neutralized.
Soft iron is used to manufacture electromagnets because it has :
A)
High retentivity
B)
High coercive field
C)
Low retentivity
D)
Low coercive field
An electromagnet is a temporary magnet that must be magnetized when current flows through the coil and demagnetized immediately when the current is switched off. To achieve this, the core material must be a 'soft' magnetic material.
1. **Coercivity (Coercive Field):** This is the intensity of the external magnetic field required to reduce the magnetization of a material to zero after it has been magnetized. A 'low coercive field' means the material loses its magnetism very easily once the external current is removed. This is essential for electromagnets to prevent them from remaining magnetized (becoming permanent magnets).
2. **Retentivity:** This is the ability of a material to retain some magnetism after the external field is removed. While low retentivity is also desirable for electromagnets, the defining characteristic that allows for the rapid switching of the magnetic state is the low coercivity.
Comparing the options:
- **High retentivity (a):** Characteristic of permanent magnets (hard magnets), not electromagnets.
- **High coercive field (b):** Characteristic of permanent magnets; it would make the electromagnet very difficult to turn off.
- **Low retentivity (c):** While soft iron has relatively low retentivity compared to steel, the primary requirement for the 'switching' action of an electromagnet is the low coercive force.
- **Low coercive field (d):** This is the most accurate technical requirement for a soft magnetic material used in electromagnets to ensure the magnetic field disappears quickly when the power is cut.
The relative permeability of paramagnetic materials is :
A)
very high
B)
slightly more than one
C)
equal to one
D)
less than one
To determine the relative permeability of paramagnetic materials, we must look at the definition of magnetic permeability and the behavior of different materials in a magnetic field:
1. **Relative Permeability (μr)**: It is defined as the ratio of the permeability of a material (μ) to the permeability of free space (μ₀), i.e., μr = μ / μ₀. It can also be expressed as μr = 1 + χ, where χ is the magnetic susceptibility.
2. **Paramagnetic Materials**: These materials have a small, positive magnetic susceptibility (χ > 0). When placed in an external magnetic field, they develop a weak magnetization in the same direction as the field. Because χ is a small positive value, μr = 1 + (small positive value), which means μr is slightly greater than 1.
3. **Analysis of Options**:
- **Option (a) 'very high'**: This describes **Ferromagnetic** materials (like iron), where μr is typically in the hundreds or thousands.
- **Option (b) 'slightly more than one'**: This correctly describes **Paramagnetic** materials (like aluminum or platinum).
- **Option (c) 'equal to one'**: This describes a **Vacuum** or non-magnetic materials.
- **Option (d) 'less than one'**: This describes **Diamagnetic** materials (like copper or bismuth), where χ is negative, making μr < 1.
The Maxwell equation VxH = J + ∂D/∂t is based on :
A)
Ampere’s law
B)
Gauss’s law
C)
Faraday’s law
D)
Coulomb’s law
The given equation $\nabla \times \mathbf{H} = \mathbf{J} + \frac{\partial \mathbf{D}}{\partial t}$ is the Maxwell-Ampère Law.
1. **Analysis of the Equation**:
- $\nabla \times \mathbf{H}$ represents the curl of the magnetic field intensity.
- $\mathbf{J}$ represents the conduction current density.
- $\frac{\partial \mathbf{D}}{\partial t}$ represents the displacement current density (introduced by James Clerk Maxwell).
2. **Why Option (a) is correct**: Ampere's original law stated that the line integral of the magnetic field around a closed loop is proportional to the electric current passing through the loop ($\nabla \times \mathbf{H} = \mathbf{J}$). Maxwell extended this by adding the term $\frac{\partial \mathbf{D}}{\partial t}$ to account for time-varying electric fields (such as those between capacitor plates), making the equation consistent with the conservation of charge. Thus, this is the generalized Ampere's Law.
3. **Why other options are incorrect**:
- **Gauss's Law (b)**: Relates the divergence of the electric field to the charge density ($\nabla \cdot \mathbf{D} = \rho$).
- **Faraday's Law (c)**: Relates the curl of the electric field to the time-varying magnetic field ($\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}$).
- **Coulomb's Law (d)**: Describes the electrostatic force between two stationary point charges, not a differential field equation.
Which one of the following is the main cause of creeping in the induction type energy meters?
A)
Friction compensation
B)
Lag/lead compensation
C)
Overload compensation
D)
Braking torque producing system
Creeping in an induction-type energy meter is a phenomenon where the disc rotates slowly even when there is no load connected (current coil is not energized), provided the voltage coil is energized. This happens because of small stray magnetic fields, over-compensation of friction, or the effect of the voltage coil's magnetic field on the disc. To prevent creeping, a 'braking torque producing system' (specifically a permanent magnet brake) is used. The permanent magnet is adjusted to provide a small amount of braking torque that opposes the motion of the disc when the driving torque is zero or very low. If the braking system is insufficient or improperly adjusted, the disc may 'creep'. Therefore, the braking torque system is the primary mechanism designed to counteract and control creeping; its absence or inadequacy is the cause of the phenomenon.
Regarding other options:
- Friction compensation (a) is used to ensure accuracy at low loads, but over-compensation can contribute to creeping; however, the 'braking system' is the specific engineering solution to stop it.
- Lag/lead compensation (b) is used to correct phase errors to ensure the meter reads energy accurately regardless of the load power factor.
- Overload compensation (c) is used to maintain accuracy when the meter is operated beyond its rated current.
The current in the RLC series circuit at resonance is :
A)
maximum
B)
minimum
C)
infinity
D)
zero
In a series RLC circuit, the total impedance (Z) is given by the formula: Z = √[R² + (X_L - X_C)²], where R is the resistance, X_L is the inductive reactance (ωL), and X_C is the capacitive reactance (1/ωC).
1. Resonance occurs when the inductive reactance equals the capacitive reactance (X_L = X_C).
2. At this condition, the term (X_L - X_C) becomes zero, and the impedance Z reduces to its minimum possible value, which is equal to the resistance R (Z = R).
3. According to Ohm's Law for AC circuits, Current (I) = V / Z.
4. Since the impedance Z is at its minimum at resonance, the current I reaches its maximum value for a given applied voltage V.
Why other options are incorrect:
- b. minimum: This occurs in a parallel RLC circuit at resonance, not a series circuit.
- c. infinity: This would require impedance to be zero, which is impossible in a real circuit due to the presence of resistance R.
- d. zero: This would require impedance to be infinite, which does not happen at resonance in a series circuit.
The depth of penetration of wave in a lossy dielectric increases with increasing :
A)
Conductivity
B)
Permeability
C)
Wavelength
D)
Permittivity
The depth of penetration, also known as the skin depth (δ), is the distance over which the amplitude of an electromagnetic wave decreases to 1/e (approximately 37%) of its original value as it penetrates a lossy medium. For a good conductor or a lossy dielectric, the formula for skin depth is given by: δ = 1 / α, where α is the attenuation constant. For a lossy medium, α is approximately proportional to the square root of the frequency (f) and the conductivity (σ), and inversely proportional to the square root of the permeability (μ) and permittivity (ε). Specifically, δ ≈ 1 / sqrt(π f μ σ). Since frequency (f) is inversely proportional to wavelength (λ) (f = c/λ), the skin depth δ is proportional to the square root of the wavelength (δ ∝ √λ). Therefore, as the wavelength increases, the depth of penetration also increases. Conversely, increasing conductivity (σ), permeability (μ), or permittivity (ε) generally leads to a decrease in the depth of penetration because they increase the attenuation of the wave within the medium.
The magnitude of electric field strength ‘E’ on a spherical surface of radius ‘r’ enclosing a charge ‘q’ is given by the expression :
A)
E = q / (4εr2)
B)
E = q / (4πr2)
C)
E = q / (4πεr2)
D)
E = q / r
To find the electric field strength 'E' on a spherical surface enclosing a charge 'q', we use Gauss's Law. Gauss's Law states that the total electric flux through a closed surface is equal to the total enclosed charge divided by the permittivity of free space (ε₀).
1. Formula for Flux: Φ = ∮ E · dA = q / ε
2. For a spherical surface of radius 'r', the electric field 'E' is constant in magnitude and perpendicular to the surface at every point. Therefore, the integral becomes: E × (Surface Area of Sphere) = q / ε
3. The surface area of a sphere is 4πr².
4. Substituting the area: E × (4πr²) = q / ε
5. Solving for E: E = q / (4πεr²)
Comparing this result to the options:
- Option (a) is missing the factor of π.
- Option (b) is missing the permittivity constant ε.
- Option (c) matches the derived formula exactly.
- Option (d) is dimensionally incorrect.
Determine the Thevenin’s equivalent circuit across terminals AB of the circuit shown below.
Wattmeter measures :
A)
apparent power
B)
true power
C)
volt ampere
D)
volt ampere reactive
A wattmeter is an instrument used to measure the active power (also known as real power or true power) in an electrical circuit.
1. **True Power (Active Power):** This is the actual power consumed by the load to perform useful work (e.g., heating or rotating a motor). It is measured in Watts (W) and is calculated as P = V * I * cos(φ), where cos(φ) is the power factor.
2. **Apparent Power (Option a):** This is the product of RMS voltage and RMS current (V * I) without considering the phase angle. It is measured in Volt-Amperes (VA). This is measured by a Voltmeter and Ammeter combined, not a wattmeter.
3. **Volt-Ampere (Option c):** This is the unit of Apparent Power, not a type of power measured by a wattmeter.
4. **Volt-Ampere Reactive (Option d):** This refers to Reactive Power (Q), which is the power that oscillates between the source and the load (stored in inductors and capacitors). It is measured in VAR and requires a VAR-meter or a power analyzer, not a standard wattmeter.
Therefore, the wattmeter specifically measures the true power.
Frequencies in UHF range propagate by means of :
A)
Sky waves.
B)
Surface waves.
C)
Ground waves.
D)
Space waves.
The propagation of electromagnetic waves depends on their frequency.
1. **UHF (Ultra High Frequency)** range spans from 300 MHz to 3 GHz. At these high frequencies, waves travel primarily in a straight line (Line-of-Sight propagation) and can penetrate the ionosphere rather than being reflected by it.
2. **Space Waves (Option d):** These are waves that travel from the transmitting antenna to the receiving antenna by a direct path (Line-of-Sight) or by reflecting off the ground. UHF waves propagate as space waves.
3. **Sky Waves (Option a):** These are waves reflected back to Earth by the ionosphere. This is characteristic of HF (High Frequency) waves (3 MHz to 30 MHz).
4. **Ground Waves / Surface Waves (Options b and c):** These are waves that follow the curvature of the Earth. This mode of propagation is effective for LF (Low Frequency) and MF (Medium Frequency) waves, typically below 30 MHz, as higher frequencies are absorbed too quickly by the ground.
Therefore, UHF frequencies propagate via space waves.
A parabolic dish antenna has a conical beam 20 wide. The directivity of the antenna is approximately:
A)
20 dB
B)
30 dB
C)
40 dB
D)
50 dB
20 dB is the best answer because it directly satisfies the fact, principle, or condition asked in the question.
Fading in ship-to-ship communication can be reduced by using which of the following?
A)
Space diversity
B)
Directional antenna
C)
Broad band antenna
D)
Frequency diversity
In ship-to-ship communication, the primary cause of fading is multipath propagation. Signals reflect off the sea surface, creating multiple paths that interfere with each other at the receiver (often resulting in Rayleigh fading).
1. **Space Diversity (Correct):** This involves using two or more antennas separated by a specific distance. Because the fading patterns are spatially dependent, it is highly unlikely that all antennas will experience a deep fade simultaneously. By combining the signals from multiple antennas, the receiver can maintain a stable connection, effectively reducing fading. This is the standard solution for maritime environments where the sea surface acts as a reflective plane.
2. **Directional Antenna (Incorrect):** While a directional antenna increases gain in one direction, it does not eliminate multipath fading caused by reflections from the water surface, and it is impractical for ships that are constantly moving and pitching/rolling.
3. **Broad band antenna (Incorrect):** Bandwidth refers to the range of frequencies an antenna can handle; it does not mitigate the physical phenomenon of multipath fading.
4. **Frequency Diversity (Incorrect):** While frequency diversity can reduce fading, it requires transmitting the same information on different frequencies. In maritime communication, space diversity is more efficient and commonly implemented via antenna arrays to combat the specific geometry of sea-surface reflections.