Past Questions — 2025

Magnetic materials are broadly classified into two categories based on their hysteresis loop and coercivity: Hard and Soft magnetic materials. 1. **Soft Magnetic Materials**: These materials have low coercivity, low retentivity, and a narrow hysteresis loop. They are easily magnetized and demagnetized, making them ideal for applications where magnetic fields must change rapidly (e.g., transformer cores, inductors). - **Silicon Steel**: An alloy of iron and silicon. The addition of silicon increases electrical resistivity and reduces hysteresis loss, making it a classic soft magnetic material used in transformer cores. - **Ferrites**: Ceramic-like compounds of iron oxide mixed with other metals. They have high electrical resistivity and low coercivity, classifying them as soft magnetic materials (specifically soft ferrites). 2. **Hard Magnetic Materials**: These have high coercivity and high retentivity, meaning they retain their magnetism even after the external field is removed. They are used to make permanent magnets. - **Alnico**: An alloy consisting of Aluminum, Nickel, and Cobalt. It is one of the most well-known hard magnetic materials used for permanent magnets. Since both Silicon steel and Ferrite are soft magnetic materials, option (d) is the correct choice.

A Permanent Magnet Moving Coil (PMMC) instrument operates on the principle of the Lorentz Force Law. When a current-carrying conductor (the moving coil) is placed within a magnetic field produced by a permanent magnet, it experiences a mechanical force. The deflecting torque (Td) is given by the formula Td = BINA, where B is the magnetic flux density, I is the current, N is the number of turns, and A is the area of the coil. This force is a direct result of the electromagnetic interaction between the magnetic field of the permanent magnet and the magnetic field generated by the current flowing through the coil. Why other options are incorrect: - a. Eddy currents: These are circulating currents induced in conductors by changing magnetic fields, usually causing losses or used in specific types of meters (like induction meters), but not for deflection in PMMC. - c. Spring control: This provides the 'controlling torque' (Tc) to oppose the deflecting torque and return the pointer to zero; it does not produce the deflection. - d. Air friction: This is a form of 'damping torque' used to prevent the pointer from oscillating, not to produce the deflection.

In the context of Current Transformers (CTs), the 'burden' refers to the total load connected to the secondary winding of the CT. This load includes the impedance of the connected measuring instruments (like ammeters), relays, and the connecting leads. 1. **Definition**: Burden is the total impedance of the secondary circuit. Since the secondary of a CT is designed to provide a specific current (usually 1A or 5A), the burden is expressed as the apparent power that the CT can deliver to the load while maintaining its specified accuracy class. 2. **Mathematical Expression**: Apparent Power (S) = I² × Z, where I is the secondary current and Z is the burden impedance. The unit for apparent power is Volt-Ampere (VA). 3. **Why other options are incorrect**: - (a) Power rating of the resistor: This refers to the heat dissipation capacity (Watts), not the load impedance seen by the CT. - (c) Current rating: This is the rated secondary current (e.g., 5A), not the load/burden. - (d) Current and voltage rating: While VA is derived from these, the standard industry term for 'burden' is specifically the VA rating.

In a series RLC circuit, the total impedance (Z) is given by the formula: Z = √[R² + (XL - XC)²], where R is the resistance, XL is the inductive reactance, and XC is the capacitive reactance. The 'total reactance' (X) of the circuit is the difference between the inductive and capacitive reactances: X = XL - XC. Resonance is defined as the condition where the inductive reactance and capacitive reactance are equal in magnitude but opposite in phase (XL = XC). Therefore, at resonance: Total Reactance = XL - XC = 0. This results in the circuit becoming purely resistive, meaning the impedance is at its minimum (Z = R) and the current is at its maximum.

Ampere's Circuital Law states that the line integral of the magnetic field (B) around any closed loop (Amperian loop) is equal to $\mu_0$ times the total current (I) passing through the surface enclosed by the loop. Mathematically, it is expressed as $\oint B \cdot dl = \mu_0 I$. This law is primarily used to calculate the magnetic field intensity produced by symmetric current distributions, such as long straight wires, solenoids, and toroids. Why other options are incorrect: - b. Electric field: The electric field is typically found using Gauss's Law for electricity. - c. Force: Magnetic force is calculated using the Lorentz force law ($F = q(E + v \times B)$) or the force between currents ($F = I L \times B$). - d. Velocity: Velocity is a kinematic property and is not the primary target of Ampere's Law.

This question is a direct application of Gauss's Law in electromagnetics. Gauss's Law states that the total electric flux (Φ) passing through any closed surface is equal to the total net charge (Q_enclosed) enclosed by that surface divided by the permittivity of free space (ε0). Mathematically, this is expressed as: Φ = ∮ E · dA = Q_enclosed / ε0. Analysis of options: - Option (a) is incorrect because the flux is only zero if the net enclosed charge is zero. - Option (b) is correct as it is the formal definition of Gauss's Law. - Option (c) is incorrect because 'Electric field times surface area' (E * A) only calculates flux if the electric field is uniform and perpendicular to the surface; it is not a general rule for all closed surfaces. - Option (d) is incorrect because potential difference is a measure of energy per unit charge between two points, not a measure of electric flux through a surface.

The velocity of an electromagnetic (EM) wave in a medium is derived from Maxwell's equations. For a non-conducting, linear, isotropic medium, the wave equation for the electric field (E) or magnetic field (H) leads to the expression for the phase velocity (v). The formula is given by v = 1 / √(με), where μ is the magnetic permeability of the medium and ε is the electric permittivity of the medium. 1. In a vacuum, μ = μ₀ (permeability of free space) and ε = ε₀ (permittivity of free space), so the speed of light c = 1 / √(μ₀ε₀) ≈ 3 × 10⁸ m/s. 2. In any other medium, the velocity decreases as μ and ε increase. Analysis of options: - Option (a) v = 1/√(με) is the mathematically correct derivation from the wave equation. - Option (b) v = √(με) is dimensionally incorrect. - Option (c) v = μ/ε is dimensionally incorrect. - Option (d) v = ε/μ is dimensionally incorrect.

To find the electric field inside a uniformly charged hollow sphere (spherical shell), 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): ∮ E · dA = Q_enclosed / ε₀. 1. Consider a Gaussian surface (an imaginary sphere) with radius 'r' located inside the hollow sphere (where r < R, and R is the radius of the shell). 2. Since the charge is distributed uniformly on the surface of the hollow sphere, there is no charge contained within the volume of the Gaussian surface (Q_enclosed = 0). 3. Substituting this into Gauss's Law: E(4πr²) = 0 / ε₀, which simplifies to E = 0. Therefore, the electric field at any point inside a uniformly charged hollow sphere is zero. Analysis of other options: - Option b (Constant): Incorrect, as the field is specifically zero, not a non-zero constant. - Option c (Increasing linearly): This occurs inside a uniformly charged solid sphere, not a hollow one. - Option d (Decreasing as 1/r²): This describes the electric field outside the sphere (r > R), where the sphere behaves like a point charge located at the center.

In instrumentation and measurements, transducers are classified into two main categories based on their power requirements: 1. **Active Transducers (Self-Generating):** These transducers generate an electrical signal (voltage or current) directly from the physical quantity being measured without requiring an external power source. Examples include thermocouples, piezoelectric crystals, and photovoltaic cells. 2. **Passive Transducers (Externally Powered):** These transducers require an external power source (excitation voltage) to operate. They typically work by changing a passive electrical property (like resistance, capacitance, or inductance) in response to a physical stimulus. Examples include strain gauges, LVDTs, and RTDs. Analysis of the options: - **a. Photo emissive cell:** These typically require an external bias to emit electrons or operate as part of a circuit; they are generally not categorized as primary self-generating active transducers in this context. - **b. Selsyn:** A Selsyn (self-synchronous) is an electromagnetic transducer used for angle measurement. It requires an AC power supply to operate, making it a passive transducer. - **c. Strain gauge:** A strain gauge works by changing its electrical resistance when stretched or compressed. It requires an external voltage source (usually via a Wheatstone bridge) to measure this change. Therefore, it is a passive transducer. - **d. Photovoltaic cell:** A photovoltaic cell converts light energy directly into electrical energy (voltage) via the photovoltaic effect. It generates its own power without needing an external source, making it a classic example of an active transducer.

Maxwell's equations are a set of four fundamental partial differential equations that form the foundation of classical electromagnetism. They are: 1. Gauss's Law for Electricity: Relates electric fields to charge densities. 2. Gauss's Law for Magnetism: States that there are no magnetic monopoles. 3. Faraday's Law of Induction: Describes how a changing magnetic field creates an electric field. 4. Ampere's Law (with Maxwell's addition of displacement current): Describes how electric currents and changing electric fields create magnetic fields. Comparing this to the options: - Option b (Gauss's Law), Option c (Faraday's Law), and Option d (Ampere's Law) are all integral components of Maxwell's equations. - Option a (Planck's Law) describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium. It is a fundamental law of Quantum Mechanics, not classical electromagnetism, and is not part of Maxwell's equations.

Step-by-step reasoning: 1. Analysis of PVC: Polyvinyl Chloride (PVC) is a synthetic plastic polymer. It is produced through the polymerization of vinyl chloride monomers, which are derived from ethylene (obtained from petroleum cracking) and chlorine. Therefore, PVC is a petroleum-based product. 2. Analysis of Mica: Mica is a naturally occurring mineral consisting of sheets of silicate. It is mined from the earth, not synthesized from petroleum. 3. Analysis of Glass: Glass is primarily made from silica (sand), soda ash, and limestone. It is an inorganic material. 4. Analysis of Porcelain: Porcelain is a ceramic material made by heating materials, generally including kaolin, feldspar, and quartz. It is a mineral-based product. Conclusion: Only PVC is derived from petroleum products.

Hysteresis loss occurs in ferromagnetic materials when they are subjected to a cycle of magnetization and demagnetization. This energy loss is caused by the internal friction encountered by magnetic domains as they reorient themselves. Mathematically, the work done per unit volume per cycle to magnetize the material is equal to the integral of H (magnetizing force) with respect to B (magnetic flux density), which is represented by the area enclosed by the B-H hysteresis loop. Therefore, the energy lost as heat per cycle is directly proportional to the area of the hysteresis loop. Why other options are incorrect: - b. Square of flux density: This is not a general rule for hysteresis loss; flux density is a variable within the loop, not the determinant of the total loss per cycle. - c. Square of current: This typically relates to copper losses (I²R losses) in electrical conductors, not magnetic hysteresis losses. - d. Magnetizing force: While the magnetizing force (H) is used to create the loop, the loss is not simply proportional to H, but to the integral of H over the full cycle of B.

1. PMMC (Permanent Magnet Moving Coil) voltmeters are passive devices. To measure voltage, they require a large series resistance (multiplier) to limit current. However, this resistance is finite, meaning the PMMC meter draws some current from the circuit being measured, which causes a 'loading effect' and introduces measurement error. 2. Electronic voltmeters (such as those based on FETs or Op-Amps) utilize high-impedance input stages. This allows them to have an extremely high input impedance (often in the Mega-ohms or Giga-ohms range). 3. A higher input impedance ensures that the voltmeter draws negligible current from the circuit under test, thereby minimizing the loading effect and providing a much more accurate reading of the actual voltage. 4. Regarding other options: (b) Electronic voltmeters are generally more complex and expensive than simple PMMC meters; (c) Electronic voltmeters require an external or internal power supply to operate the active components, whereas PMMC meters are self-powered by the circuit; (d) While they may have different stability characteristics, the primary and most significant advantage in measurement theory is the input impedance.

The Superposition Theorem states that in a linear bilateral network containing multiple independent sources, the current through (or voltage across) any element is the algebraic sum of the currents (or voltages) produced by each source acting alone, while all other independent sources are replaced by their internal impedances. 1. **Linearity**: The theorem relies on the principle of linearity. Voltage (V) and Current (I) are linear responses in a linear circuit. Therefore, options (a) and (b) are valid applications of the theorem. 2. **Non-linearity of Power**: Power (P) is calculated as P = I²R or P = V²/R or P = VI. Because power depends on the square of the current or voltage, it is a non-linear (quadratic) function. 3. **Mathematical Proof**: If two sources produce currents I1 and I2 respectively, the total current is I = I1 + I2. The total power is P_total = (I1 + I2)²R = (I1² + I2² + 2I1I2)R. However, the sum of individual powers would be P1 + P2 = I1²R + I2²R. Since (I1 + I2)²R ≠ I1²R + I2²R (unless one current is zero), the superposition theorem cannot be applied to power.

Creeping in an induction-type energy meter is a phenomenon where the aluminum disc rotates slowly even when there is no load connected (current is zero). This occurs because of a small driving torque produced by the voltage coil or other external factors. 1. **Why 'Light falling on the disc' is correct:** When light falls on the disc, it can cause uneven heating of the aluminum disc. This creates convection currents in the surrounding air, which can exert a mechanical force on the disc, causing it to rotate slowly. This is a known cause of creeping. 2. **Other causes of creeping:** Other common causes include over-voltage (which can cause the voltage coil to produce enough torque to overcome friction), friction imbalances, or stray magnetic fields. 3. **Why other options are incorrect:** - **Overload (a):** Overloading increases the current, which increases the speed of the disc; it does not cause the disc to rotate at zero load. - **Overvoltage (b):** While overvoltage *can* contribute to creeping, in the context of standard multiple-choice questions for electrical measurements, 'light falling on the disc' is a classic specific cause cited for the physical movement of the disc under no-load conditions. However, if 'Overvoltage' and 'Light' are both present, 'Light' is often the intended answer for specific 'creeping' mechanisms related to thermal effects. - **Low load conditions (d):** Creeping specifically refers to rotation at *zero* load. Low load simply means the meter is operating normally at a low rate.

The correct answer is **Ampere–Maxwell Law**. Maxwell modified Ampere’s law by adding the **displacement current** term, \(\varepsilon_0 \frac{d\Phi_E}{dt}\), to account for time-varying electric fields and to make the law consistent with charge conservation. This is the equation that introduces the concept of displacement current. Why the others are incorrect: - **Gauss’s Law for Magnetism**: states that the net magnetic flux through a closed surface is zero, meaning there are no magnetic monopoles. It does not involve displacement current. - **Faraday’s Law**: relates a changing magnetic field to an induced electric field. It describes electromagnetic induction, not displacement current. - **Gauss’s Law**: relates electric flux to enclosed charge. It does not introduce displacement current.

Thevenin's Theorem is a fundamental principle in network analysis used to simplify a complex linear circuit into a simple equivalent circuit. According to the theorem, any combination of voltage sources, current sources, and resistors with two terminals can be replaced by a single voltage source (called the Thevenin Voltage, Vth) connected in series with a single resistor (called the Thevenin Resistance, Rth). Breakdown of options: - Option (a) is correct: This is the definition of a Thevenin equivalent circuit. - Option (b) is incorrect: A current source in parallel with a resistor describes Norton's Theorem, not Thevenin's. - Option (c) is incorrect: Thevenin's theorem deals with resistive networks (or impedance in AC), but the standard definition for basic network theory refers to a resistor, not a capacitor. - Option (d) is incorrect: A resistor only would imply the network has no active sources, which is not the general case for Thevenin's theorem.

To find the pressure at a certain depth in a fluid, we use the hydrostatic pressure formula: P = ρgh or P = (S × ρ_water) × g × h. 1. **Given Data:** - Specific gravity of oil (S) = 0.8 - Depth (h) = 4 m - Density of water (ρ_water) ≈ 1000 kg/m³ - Acceleration due to gravity (g) ≈ 9.81 m/s² 2. **Calculate Density of Oil (ρ_oil):** ρ_oil = Specific Gravity × Density of Water ρ_oil = 0.8 × 1000 kg/m³ = 800 kg/m³ 3. **Calculate Pressure (P):** P = ρ_oil × g × h P = 800 kg/m³ × 9.81 m/s² × 4 m P = 31,392 N/m² 4. **Convert to kN/m²:** P = 31,392 / 1000 = 31.392 kN/m² Rounding to one decimal place, we get 31.4 kN/m². Comparing this result to the options: - Option (a) 31.4 kN/m² matches our calculation. - Options (b), (c), and (d) are incorrect as they do not align with the physical properties of oil with a specific gravity of 0.8 at the given depth.

The goal of removing organic matter from wastewater is typically achieved through biological treatment. 1. **Activated Sludge Process (Option b):** This is a widely used secondary treatment method. It employs a biological process where a mass of microorganisms (activated sludge) is mixed with wastewater in an aeration tank. These microbes consume and break down the biodegradable organic matter (measured as BOD - Biochemical Oxygen Demand), converting it into carbon dioxide, water, and new biomass. This is the standard method for organic matter removal. 2. **Reverse Osmosis (Option a):** This is a membrane filtration process used primarily for desalination or removing dissolved salts and very small molecules. While it can remove organic molecules, it is an advanced tertiary treatment and is not the 'common' method for bulk organic matter removal due to high energy costs and membrane fouling. 3. **Ion Exchange (Option c):** This process is used to remove specific dissolved ions (like hardness ions Ca2+ and Mg2+ or nitrates) by exchanging them with other ions. It is not used for the general removal of organic matter. 4. **Ultrafiltration (Option d):** This is a pressure-driven membrane process that removes suspended solids, bacteria, and high-molecular-weight organics. However, it cannot remove dissolved organic matter as effectively as biological processes and is generally used for polishing or pretreatment rather than primary organic removal.

The fundamental distinction between a solid and a fluid (liquids and gases) lies in their response to shear stress. 1. **Solid Behavior**: When a shear stress is applied to a solid, it undergoes a finite deformation (strain). If the stress is removed (within the elastic limit), it returns to its original shape. A solid can resist shear stress by maintaining a static equilibrium of deformation. 2. **Fluid Behavior**: A fluid is defined as a substance that deforms continuously (flows) when subjected to a shear stress, no matter how small that stress may be. In other words, a fluid cannot resist shear stress while remaining at rest; it will continue to deform as long as the stress is applied. **Analysis of Options:** - **Option a**: Incorrect. Solids resist shear stress by deforming to a fixed point; fluids cannot resist it statically. - **Option b**: Incorrect. A fixed shape is a characteristic of a solid, not a fluid. - **Option c**: Correct. This is the defining physical property of a fluid. - **Option d**: Incorrect. While gases (fluids) are highly compressible, liquids (also fluids) are generally considered incompressible. Therefore, compressibility is not the universal property that distinguishes all fluids from solids.

The drainage coefficient is defined as the depth of water to be removed from a given area per unit of time to prevent crop damage or to maintain the water table at a desired depth. Mathematically, it is the volume of water removed per unit area per unit time. Since Volume/Area = Depth, the unit of the drainage coefficient is a unit of length (depth) per unit of time. In irrigation and drainage engineering, this is most commonly expressed as centimeters per day (cm/day) or millimeters per day (mm/day). Analysis of options: - Option (a) T/day: 'T' usually refers to tonnes, which is a unit of mass, not depth. - Option (b) m3/day: This is a unit of discharge (volume per time), not a coefficient based on area. - Option (c) cm/day: Correct. It represents the depth of water removed per day. - Option (d) cm/km: This is a unit of slope or gradient, not a rate of water removal.

Step-by-step calculation: 1. **Identify Given Data**: - Shape of Direct Runoff Hydrograph (DRH): Triangular - Base period (T) = 80 hours - Peak flow rate (Qp) = 30 m³/sec - Catchment area (A) = 86.4 km² = 86.4 × 10⁶ m² 2. **Calculate Total Volume of Runoff (V)**: For a triangular hydrograph, the volume is the area under the triangle: Volume (V) = 1/2 × Base × Height V = 1/2 × (80 hours × 3600 sec/hour) × 30 m³/sec V = 0.5 × 288,000 sec × 30 m³/sec V = 4,320,000 m³ 3. **Calculate Rainfall Excess (Depth of Runoff)**: The rainfall excess (d) is the total volume of runoff divided by the catchment area: d = Volume / Area d = 4,320,000 m³ / 86,400,000 m² d = 0.05 meters 4. **Convert to Centimeters**: d = 0.05 m × 100 cm/m = 5 cm Conclusion: The rainfall excess that resulted in the hydrograph is 5 cm. Therefore, option (b) is correct.

Dynamic viscosity (μ) is defined by Newton's Law of Viscosity as the ratio of shear stress (τ) to the velocity gradient (du/dy). 1. Formula: μ = τ / (du/dy) 2. Units of Shear Stress (τ): Force per unit area = N/m² = (kg·m/s²) / m² = kg/(m·s²) 3. Units of Velocity Gradient (du/dy): (m/s) / m = 1/s 4. Calculating the unit of μ: [kg/(m·s²)] / [1/s] = kg/(m·s). Analysis of options: - Option (a) kg/m·s: This is the derived SI unit for dynamic viscosity. It is also equivalent to Pascal-seconds (Pa·s). - Option (b) N·s/m²: While N·s/m² is mathematically equivalent to Pa·s (since 1 Pa = 1 N/m²), the standard base SI unit representation is kg/(m·s). However, in many contexts, Pa·s is used. In this specific multiple-choice set, kg/m·s is the fundamental base unit representation. - Option (c) m²/s: This is the SI unit for Kinematic Viscosity (ν = μ/ρ). - Option (d) kg/m³: This is the SI unit for Density (ρ).

Turbidity is an optical property of water that describes the cloudiness or haziness of a fluid caused by individual particles (suspended solids) that are generally invisible to the naked eye. 1. **Why Option (d) is correct:** Turbidity is primarily caused by suspended inorganic matter such as finely divided particles of clay, silt, and other minerals. These particles scatter light, preventing it from passing through the water in a straight line, which results in the appearance of turbidity. 2. **Why other options are incorrect:** - **Algae (a):** While algae can contribute to turbidity (biological turbidity), the primary and most common cause of turbidity in general water quality contexts is inorganic suspended solids. Algae are typically categorized under biological contaminants or specific 'algal blooms'. - **Fungi (b):** Fungi are not a primary cause of water turbidity in standard environmental water sources. - **Organic salts (c):** Dissolved salts (whether organic or inorganic) do not cause turbidity because they are dissolved at the molecular or ionic level and do not scatter light. Only suspended particles cause turbidity.

Bernoulli's principle states that for an inviscid, incompressible fluid in steady flow, the sum of pressure energy, kinetic energy, and potential energy per unit volume remains constant along a streamline. Mathematically, it is expressed as: P + ½ρv² + ρgh = constant. This is a direct application of the Law of Conservation of Energy. Why other options are incorrect: - Option (a) Conservation of mass is the basis for the 'Continuity Equation' (A1V1 = A2V2). - Option (b) 'Conservation of pressure' is not a recognized fundamental law of physics; pressure changes as energy transforms between kinetic and potential forms. - Option (c) Conservation of momentum is the basis for the 'Momentum Equation' or 'Euler's Equation' used to calculate forces exerted by flowing fluids.