← MES Jr. Grade
Past Questions
If the reactance ‘X’ of the line could be varied and the resistance ‘R’ remaining constant, the maximum steady state power that could be transmitted over the line would be greatest when
A)
X=√3R
B)
R=√3X
C)
X=R
D)
R=X/√3
The steady-state power transmitted over a lossless or lossy line is given by the formula: P = (V_s * V_r / Z) * sin(θ - α) / (1 - (V_s * V_r / Z^2) * sin^2(θ - α)), where Z is the impedance (Z = √(R² + X²)) and α is the impedance angle (tan α = X/R).
For a line with constant resistance R and variable reactance X, the maximum power transfer occurs when the receiving end voltage is adjusted or the load angle is optimized. Specifically, the condition for maximum power transfer in a transmission line (considering the effect of resistance) is derived by differentiating the power expression with respect to X.
Mathematically, for a fixed R, the maximum power that can be transmitted is maximized when the impedance angle α is 30°.
Since tan(α) = X/R, for α = 30°:
tan(30°) = X/R
1/√3 = X/R
Therefore, R = √3X.
At this specific ratio, the line is optimized to deliver the highest possible steady-state power given the constraint of a fixed resistance.
The winding short-circuit fault protection of a transformer can be achieved by
A)
mho relay
B)
distance relay
C)
directional relay
D)
differential relay
A winding short-circuit fault (internal fault) in a transformer occurs when there is a failure of insulation between turns or between the winding and the core/tank. The most effective way to detect this is by comparing the current entering the transformer with the current leaving it.
1. **Differential Relay (Correct):** This relay operates on the principle of Kirchhoff's Current Law. Under normal conditions or external faults, the difference between the primary and secondary currents (after accounting for the turns ratio) is zero. If an internal short-circuit occurs, the balance is disturbed, and a differential current flows through the relay coil, triggering the circuit breaker. It is the standard protection for internal transformer faults.
2. **Mho Relay (Incorrect):** This is a type of distance relay primarily used for the protection of long transmission lines to detect phase-to-phase or phase-to-ground faults.
3. **Distance Relay (Incorrect):** These relays measure the impedance of the line. They are used for transmission line protection, not for internal transformer winding faults.
4. **Directional Relay (Incorrect):** These relays are used to determine the direction of power flow and are typically used in ring mains or parallel feeders to isolate a faulted section while keeping the rest of the network energized.
Then negative phase sequence in a three phase synchronous motor exists when the motor is
A)
under loaded
B)
overloaded
C)
supplied with unbalanced voltage
D)
hot
In a three-phase system, the concept of sequence components (Positive, Negative, and Zero sequence) is used to analyze unbalanced conditions.
1. **Positive Sequence**: This occurs when the three phases are balanced and have the same phase sequence as the motor's design. It produces a rotating magnetic field that rotates in the intended direction of the motor.
2. **Negative Sequence**: This occurs when the phase sequence is reversed relative to the positive sequence. In a synchronous motor, a negative sequence component is created specifically when the supply voltages are unbalanced (i.e., the magnitudes of the voltages are different or the phase angles between them are not exactly 120 degrees).
3. **Effect**: The negative sequence field rotates in the opposite direction to the rotor's rotation. This induces double-frequency currents in the rotor, leading to overheating and torque pulsations.
Analysis of options:
- (a) Under loaded: Loading conditions affect the current magnitude and power factor, but not the phase sequence of the supply voltage.
- (b) Overloaded: Overloading leads to increased current and potential overheating, but it does not create a negative phase sequence unless the overload causes a phase failure or severe voltage drop in one phase.
- (c) Supplied with unbalanced voltage: This is the direct cause of negative sequence components according to Fortescue's Theorem of Symmetrical Components.
- (d) Hot: Temperature is a result of losses (including those from negative sequence currents), not a cause of the sequence itself.
As compared to closed loop system, an open loop system is
A)
more stable as well as more accurate
B)
less stable as well as less accurate
C)
more stable but less accurate
D)
less stable but more accurate
To determine the correct answer, we must compare the fundamental characteristics of Open-Loop and Closed-Loop control systems:
1. **Stability**: Open-loop systems are generally more stable. This is because they do not utilize feedback. In closed-loop systems, the feedback loop can potentially introduce instability (oscillations) if the gain is too high or if there are significant phase shifts in the system, leading to a positive feedback condition.
2. **Accuracy**: Closed-loop systems are significantly more accurate. Because they monitor the output and compare it with the desired reference (error detection), they can automatically correct for disturbances and internal parameter variations. An open-loop system has no way to detect if the output has deviated from the desired value and cannot correct itself, making it less accurate.
Comparing the two:
- Open Loop: High Stability, Low Accuracy.
- Closed Loop: Potential for Instability, High Accuracy.
Therefore, an open-loop system is more stable but less accurate than a closed-loop system.
The magnitude of voltage at the sending end of a long transmission line becomes higher than the voltage magnitude at the receiving end, this phenomena is called
A)
Hunting effect
B)
Corona effect
C)
Ferranti effect
D)
Voltage instability effect
The phenomenon where the receiving end voltage ($V_r$) becomes higher than the sending end voltage ($V_s$) in a long transmission line under no-load or light-load conditions is known as the Ferranti Effect. This occurs because the line's capacitance creates a charging current that leads the voltage; when the line is lightly loaded, this current flows through the line inductance, causing a voltage rise toward the receiving end.
Analysis of other options:
- a. Hunting effect: This refers to the oscillation of the rotor of a synchronous machine around its equilibrium position due to sudden load changes.
- b. Corona effect: This is the ionization of air surrounding a high-voltage conductor, resulting in a violet glow and power loss.
- d. Voltage instability effect: This is a general condition where the system cannot maintain an acceptable voltage profile under a given load demand, often leading to voltage collapse.
What is incorrect statement about a power transformer?
A)
It is designed to have maximum efficiency at or near full load
B)
It is designed to have considerably greater leakage reactance
C)
It isolates the generating plant from the transmission line electrically
D)
It is designed to have maximum efficiency at or near half load
To determine the incorrect statement, let's analyze the characteristics of a power transformer:
1. **Efficiency and Loading (Options a and d):** Power transformers are used in transmission networks and are typically operated at or near their rated capacity (full load) for long periods. Therefore, they are specifically designed to achieve maximum efficiency at or near full load to minimize energy losses during bulk power transfer. Statement (a) is correct, and statement (d) is incorrect.
2. **Leakage Reactance (Option b):** Power transformers are designed to have a higher leakage reactance compared to distribution transformers. This is necessary to limit the short-circuit currents that can occur during faults in the high-voltage transmission system, protecting the equipment from catastrophic failure. Statement (b) is correct.
3. **Electrical Isolation (Option c):** One of the primary functions of a transformer is to provide galvanic isolation between the primary (generating plant) and secondary (transmission line) circuits, while still allowing the transfer of energy via electromagnetic induction. Statement (c) is correct.
Since the question asks for the INCORRECT statement, option (d) is the right choice.
What material is used in the breather of a transformer to absorb moisture content of air entering into the transformer’s oil contact area?
A)
Calcium carbonate
B)
Silica gel
C)
Sodium chloride
D)
Carbon crystals
In a transformer, the oil expands and contracts due to temperature changes during operation. As the oil level fluctuates, air is drawn in and pushed out of the conservator tank. To prevent moisture from entering the oil (which would lower the dielectric strength and cause insulation failure), a 'breather' is used. The breather contains Silica Gel, a desiccant material that has a high affinity for water molecules. Silica gel absorbs moisture from the incoming air, ensuring that only dry air enters the transformer. When the silica gel becomes saturated with moisture, it changes color (typically from blue to pink), indicating that it needs to be replaced or reheated to remove the moisture.
Why other options are incorrect:
- Calcium carbonate (a) is primarily used in construction or as a filler; it is not a desiccant.
- Sodium chloride (c) is common table salt; it does not possess the porous structure required to act as an effective industrial desiccant for transformer breathers.
- Carbon crystals (d) are conductive materials and are not used for moisture absorption.
In force-current analogy, mass is analogous to
A)
Inductance
B)
Current
C)
Voltage
D)
Capacitance
In system modeling, analogies are used to relate mechanical systems to electrical systems. There are two primary types of analogies: Force-Voltage (f-v) and Force-Current (f-i).
1. **Force-Current (f-i) Analogy**: In this analogy, the force (F) in a mechanical system is analogous to current (i) in an electrical system.
- The governing equation for a mass (M) in a mechanical system is F = M(dv/dt).
- The governing equation for an inductor (L) in an electrical system is v = L(di/dt).
- However, in the f-i analogy, we look at the relationship where the 'effort' (force) is mapped to 'flow' (current). In this specific mapping, Mass (M) is analogous to Inductance (L) because both represent the energy-storing element that opposes changes in the flow (velocity in mechanical, current in electrical).
2. **Comparison Table for Force-Current (f-i) Analogy**:
- Force (F) $\rightarrow$ Current (i)
- Mass (M) $\rightarrow$ Inductance (L)
- Viscous Friction (B) $\rightarrow$ Conductance (1/R)
- Spring Constant (K) $\rightarrow$ Reciprocal of Capacitance (1/C)
- Velocity (v) $\rightarrow$ Voltage (v)
- Displacement (x) $\rightarrow$ Magnetic Flux ($\Phi$)
Therefore, mass is analogous to inductance in the force-current analogy. Option (a) is correct. Options (b), (c), and (d) represent other electrical parameters that do not map to mass in this specific analogy.
The complex conjugate poles of a transfer function lie on the left half of the s-plane, the system is
A)
stable
B)
marginally stable
C)
unstable
D)
may be stable or unstable
In control system theory, the stability of a linear time-invariant (LTI) system is determined by the location of the poles of its transfer function in the s-plane.
1. **Stable System**: A system is considered absolutely stable if all poles of the transfer function lie strictly in the Left Half of the s-plane (LHP). This ensures that the impulse response of the system decays to zero as time approaches infinity (e.g., terms like e^(-at) where a > 0).
2. **Marginally Stable System**: A system is marginally stable if there are non-repeated poles on the imaginary axis (jω-axis) and no poles in the Right Half Plane (RHP). This results in sustained oscillations.
3. **Unstable System**: A system is unstable if at least one pole lies in the Right Half Plane (RHP) or if there are repeated poles on the imaginary axis. This leads to an exponentially growing response.
In this specific question, it is stated that the complex conjugate poles lie on the left half of the s-plane. Since all poles are in the LHP, the system is stable.
Which of the following DC generators at load condition offers poorest voltage regulation?
A)
Cumulative compounded generator
B)
Series generator
C)
Shunt generator
D)
Differential compounded generator
Voltage regulation is a measure of the change in terminal voltage from no-load to full-load. A 'poor' voltage regulation in the context of DC generators typically refers to a significant drop in voltage as load increases.
1. **Shunt Generator (c):** The terminal voltage drops slightly due to armature resistance (IR drop) and armature reaction. It has moderate regulation.
2. **Series Generator (b):** The terminal voltage actually increases as the load increases because the load current increases the field flux. This is 'rising' regulation.
3. **Cumulative Compounded Generator (a):** The series field aids the shunt field. Depending on the design, it can be constant-voltage, under-compounded (slight drop), or over-compounded (slight rise). It generally offers the best (most stable) regulation.
4. **Differential Compounded Generator (d):** In this machine, the series field opposes the shunt field. As the load current increases, the series field flux subtracts from the shunt field flux, causing the terminal voltage to drop sharply. Because the voltage decreases rapidly with an increase in load, it exhibits the poorest (most severe) voltage drop, making it the correct answer.
The corona loss in a three-phase transmission line does not depend upon the parameter
A)
thickness of the conductor
B)
power frequency
C)
distance between the conductors
D)
phase-sequence
Corona loss in a transmission line is the power loss caused by the ionization of air surrounding the conductor when the electric field intensity exceeds the dielectric strength of air. The formula for corona power loss (Peek's formula) is given by: P = (24.1) * f * m * d * (V - Vc)^2 * 10^-5 kW/km, where f is the power frequency, m is the number of phases, d is the diameter of the conductor, and V is the operating voltage.
1. Thickness of the conductor (Option a): The diameter (d) of the conductor directly affects the electric field intensity at the surface. A thicker conductor reduces the field intensity, thereby affecting corona loss.
2. Power frequency (Option b): As seen in the formula, corona loss is directly proportional to the frequency (f) of the AC supply.
3. Distance between the conductors (Option c): The spacing between conductors affects the critical disruptive voltage (Vc). If conductors are closer, the electric field is modified, influencing when corona begins and the magnitude of the loss.
4. Phase-sequence (Option d): The phase sequence (e.g., R-Y-B or R-B-Y) refers to the order in which the voltages reach their peak values in a three-phase system. It has no physical impact on the electric field intensity around an individual conductor or the ionization of the surrounding air. Therefore, corona loss is independent of the phase sequence.
The characteristics equation of a closed-loop control system is given as s^2+4s+16 =0. The resonant frequency in radians/sec. of the system is
A)
2
B)
2/3
C)
4
D)
2/2
Step-by-step solution:
1. The standard characteristic equation for a second-order control system is given by: s^2 + 2ζωn s + ωn^2 = 0, where ζ is the damping ratio and ωn is the undamped natural frequency.
2. Comparing the given equation s^2 + 4s + 16 = 0 with the standard form:
- ωn^2 = 16 => ωn = √16 = 4 rad/sec
- 2ζωn = 4 => 2 * ζ * 4 = 4 => ζ = 4/8 = 0.5
3. The resonant frequency (ωr) for a second-order system is the frequency at which the peak magnitude of the frequency response occurs. It is calculated using the formula:
ωr = ωn * √[1 - 2ζ^2]
4. Substituting the values of ωn and ζ:
ωr = 4 * √[1 - 2(0.5)^2]
ωr = 4 * √[1 - 2(0.25)]
ωr = 4 * √[1 - 0.5]
ωr = 4 * √0.5
ωr = 4 * 0.707 ≈ 2.828 rad/sec.
Observation on Options:
Looking at the provided options (a. 2, b. 2/3, c. 4, d. 2/2), the calculated resonant frequency (2.828) is not explicitly listed. However, in many competitive exams, if the question asks for 'resonant frequency' but the options align with the 'natural frequency' (ωn), it is a common nomenclature error in the question paper.
- Natural Frequency (ωn) = 4 rad/sec (Matches Option c).
- Resonant Frequency (ωr) = 2.828 rad/sec (No match).
Given the options provided, the examiner intended to ask for the natural frequency (ωn), making option (c) the intended correct answer.
The charge carrier available in a semiconductor material
A)
free electron and holes
B)
free electrons only
C)
holes only
D)
positively charged ions
In semiconductor physics, electrical conduction is carried out by two types of charge carriers: electrons and holes.
1. **Free Electrons**: These are electrons that have gained enough energy to break away from their covalent bonds in the valence band and move into the conduction band, where they can move freely through the crystal lattice. They carry a negative charge.
2. **Holes**: When an electron leaves its position in the valence band to become a free electron, it leaves behind a vacancy or a 'hole'. This vacancy acts as a positive charge carrier because an electron from a neighboring atom can move to fill it, effectively moving the hole in the opposite direction.
In intrinsic (pure) semiconductors, the number of free electrons equals the number of holes. In extrinsic (doped) semiconductors, one type of carrier dominates (electrons in n-type, holes in p-type), but both are fundamentally the charge carriers available in the material.
- Option (b) is incorrect because it ignores holes, which are essential for p-type conduction.
- Option (c) is incorrect because it ignores electrons, which are essential for n-type conduction.
- Option (d) is incorrect because ions are fixed in the crystal lattice (especially in doped semiconductors) and do not act as mobile charge carriers for current flow.
Which is the correct statement related to the Gauss’s law?
A)
The electric force between two charge particles is proportional to the product of the charges on two particles.
B)
The total electric flux through any closed surface is equal to the total charge enclosed by that surface.
C)
The electric field intensity is the force per unit charge in free space.
D)
The electric flux density is the measure of electric field intensity.
Gauss’s law states that the total electric flux through any closed surface is equal to the total charge enclosed by that surface divided by the permittivity of free space (∮E·dA = Q_enclosed/ε0). Hence option **b** is the correct statement in essence, since it identifies the closed-surface flux as being determined by the enclosed charge.
Why the others are incorrect:
- **a** describes Coulomb’s law: the electric force between two point charges is proportional to the product of the charges (and inversely proportional to the square of distance), not Gauss’s law.
- **c** is the definition of electric field intensity, not Gauss’s law.
- **d** is incorrect because electric flux density (D) is not a measure of electric field intensity (E); rather, D = εE in a linear medium.
An AC voltage of magnitude 20 V is applied to a circuit consisting of a resistor and an inductive coil with a negligible resistance. If the voltage across resistor is 12 V, the voltage across the coil is
A)
6V
B)
8V
C)
10V
D)
16V
1. Analysis of the Circuit: The circuit consists of a resistor (R) and an inductive coil with negligible resistance (pure inductor L) connected in series.
2. Phasor Relationship: In a series RL circuit, the voltage across the resistor (Vr) and the voltage across the inductor (Vl) are 90 degrees out of phase. The total applied voltage (Vs) is the phasor sum of these two voltages.
3. Mathematical Formula: The relationship is given by the Pythagorean theorem: Vs² = Vr² + Vl².
4. Given Values:
- Total applied voltage (Vs) = 20 V
- Voltage across resistor (Vr) = 12 V
5. Calculation:
Vl² = Vs² - Vr²
Vl² = (20)² - (12)²
Vl² = 400 - 144
Vl² = 256
Vl = √256 = 16 V.
6. Conclusion: The voltage across the coil is 16 V. Options a, b, and c are incorrect because they do not satisfy the phasor sum requirement for an RL circuit.
‘Creep’ in energy meters can be prevented by
A)
using extra turns on the voltage coil
B)
having two holes on opposite sides of the disc
C)
using a stronger brake magnet
D)
using steel laminations of high permeability
Creep in an induction-type energy meter is a phenomenon where the disc continues to rotate slowly even when there is no load current flowing (i.e., the current coil is not energized). This happens due to small stray magnetic fields, friction imbalances, or over-compensation of the brake magnet.
To prevent creep, two holes are drilled on opposite sides of the aluminum disc. When the disc is at rest, these holes create an asymmetry in the eddy current distribution and the resulting torque. This creates a 'dead band' or a stable equilibrium position where the driving torque is insufficient to overcome the frictional torque and the magnetic imbalance caused by the holes. Consequently, the disc will not rotate unless a minimum load current is applied.
Analysis of other options:
- Option (a): Extra turns on the voltage coil would increase the driving torque from the voltage coil, potentially worsening the creep.
- Option (c): While a stronger brake magnet increases the braking torque, it does not eliminate the possibility of creep and would affect the overall calibration/accuracy of the meter.
- Option (d): High permeability laminations are used to reduce hysteresis and eddy current losses in the core, but they do not address the mechanical/magnetic instability that causes creep.
Which of the following represents the Maxwell’s continuity equation for time varying electromagnetic fields
A)
∇·J + ∂ρ/∂t = 0
B)
∇·J = ρ
C)
∇×E = 0
D)
None of these
The continuity equation is a mathematical statement of the law of conservation of charge. It states that the current flowing out of a closed surface (divergence of current density J) must be equal to the rate of decrease of the charge enclosed within that surface.
Mathematically, the net current flowing out of a volume is given by the volume integral of the divergence of current density: ∫(∇·J)dV. According to the conservation of charge, this must equal the negative rate of change of total charge Q: -dQ/dt. Since Q = ∫ρdV, we have ∫(∇·J)dV = -∂/∂t ∫ρdV. For this to hold for any arbitrary volume, the integrands must be equal: ∇·J = -∂ρ/∂t, which rearranges to ∇·J + ∂ρ/∂t = 0.
Analysis of other options:
- Option (b) ∇·J = ρ is incorrect; it does not represent a standard physical law in electromagnetics.
- Option (c) ∇×E = 0 represents the electrostatic condition (where the electric field is conservative), but in time-varying fields, ∇×E = -∂B/∂t (Faraday's Law).
The driving point impedance function Z(s)= s/(s^2+1) can be realized as a
A)
R-C network
B)
R-L network
C)
L-C network
D)
R-L-C network
To determine the type of network that can realize the driving point impedance function Z(s) = s / (s^2 + 1), we analyze the properties of the function based on network synthesis theory:
1. **Analysis of the Function**: The given function is Z(s) = s / (s^2 + 1).
2. **Lossless Network Condition**: A network is lossless (consisting only of Inductors (L) and Capacitors (C)) if its driving point impedance Z(s) is a lossless function. A function is lossless if:
- It is a rational function of s.
- All its poles and zeros are simple and lie on the imaginary axis (jω axis).
- The poles and zeros alternate between the origin and infinity along the imaginary axis.
3. **Checking the Poles and Zeros**:
- **Zeros**: Set the numerator to zero: s = 0. There is a simple zero at the origin.
- **Poles**: Set the denominator to zero: s^2 + 1 = 0 => s = ±j1. There are simple poles on the imaginary axis at s = j and s = -j.
4. **Alternation Property**:
- Zero at s = 0
- Pole at s = ±j1
- (The next zero would be at infinity)
Since the poles and zeros are simple, lie on the imaginary axis, and alternate, Z(s) is a lossless function.
5. **Conclusion**: A lossless driving point impedance function can be realized using only L and C elements. If the function had real parts in the poles/zeros or coefficients that implied energy dissipation, it would require resistors (R). Since this function is purely imaginary for s = jω (Z(jω) = jω / (1 - ω^2)), it represents a purely reactive network.
Therefore, the network is an L-C network.
Which of the following magnetic materials have small area of hysteresis loop?
A)
Saturable magnetic material
B)
Soft magnetic material
C)
Hard magnetic material
D)
Diamagnetic material
The area of a hysteresis loop represents the energy loss (hysteresis loss) per unit volume per cycle of magnetization.
1. **Soft Magnetic Materials**: These materials are characterized by easy magnetization and demagnetization. They have low coercivity (the intensity of the magnetic field required to reduce magnetization to zero) and low retentivity. Consequently, the hysteresis loop is narrow, meaning the area is small, resulting in low energy loss. Examples include soft iron and permalloy. These are ideal for transformer cores and electromagnets.
2. **Hard Magnetic Materials**: These materials are difficult to magnetize and demagnetize. They have high coercivity and high retentivity, resulting in a wide hysteresis loop with a large area. This indicates high energy loss per cycle. Examples include Alnico and ferrite. These are used to make permanent magnets.
3. **Saturable Magnetic Materials**: This refers to a state of magnetization rather than a specific class of material defined by loop area. All ferromagnetic materials eventually saturate.
4. **Diamagnetic Materials**: These materials do not exhibit a hysteresis loop because they do not retain magnetization after the external field is removed; they show a very weak, negative response to magnetic fields.
A wire conductor of resistance 1 Ω is doubled in length. Its resistance becomes
A)
the same as that when cold
B)
higher than cold resistance
C)
lower than cold resistance
D)
higher or lower than the cold resistance depending on the supply frequency
The resistance (R) of a conductor is governed by the formula R = ρ(L/A), where ρ is the resistivity of the material, L is the length, and A is the cross-sectional area.
1. According to the formula, resistance is directly proportional to length (R ∝ L).
2. If the length of the wire is doubled (L becomes 2L), the resistance will also double (R becomes 2Ω), assuming the cross-sectional area and material remain constant.
3. Since 2 Ω is greater than the original 1 Ω (which represents the initial or 'cold' state of the wire), the resistance becomes higher.
Regarding the options:
- Option (a) is incorrect because resistance changes with length.
- Option (b) is correct because doubling the length increases the resistance.
- Option (c) is incorrect because resistance increases, not decreases, with length.
- Option (d) is incorrect because DC resistance of a wire is independent of supply frequency.
Which parameter represents the relationship between output current and output voltage in a two-port network?
A)
Z—Parameter
B)
Y—Parameter
C)
H—Parameter
D)
G—Parameter
In network theory, two-port network parameters are used to describe the relationship between the voltages and currents at the input and output ports.
1. **Y-Parameters (Admittance Parameters):** These are defined by expressing the currents ($I_1$ and $I_2$) as functions of the voltages ($V_1$ and $V_2$). The equations are:
$I_1 = Y_{11}V_1 + Y_{12}V_2$
$I_2 = Y_{21}V_1 + Y_{22}V_2$
Here, the output current ($I_2$) is expressed as a function of the input voltage ($V_1$) and output voltage ($V_2$). Specifically, $Y_{22}$ represents the relationship between the output current and output voltage when the input is open-circuited. Thus, Y-parameters fundamentally relate currents to voltages.
2. **Z-Parameters (Impedance Parameters):** These express voltages as functions of currents ($V = ZI$). They represent the relationship between output voltage and output current (the inverse of the question's requirement).
3. **H-Parameters (Hybrid Parameters):** These are a mix, expressing $V_1$ and $I_2$ as functions of $I_1$ and $V_2$. While they involve output current and voltage, they are specifically designed for transistor modeling rather than a general current-to-voltage relationship for the output port.
4. **G-Parameter:** This is not a standard primary two-port network parameter in the same category as Z, Y, H, and ABCD parameters.
Therefore, the parameter that represents the relationship where current is the dependent variable and voltage is the independent variable (specifically for the output) is the Y-parameter.
The potential at a point due to a charge is 9 V. If the distance from the charge is increased 3 times, the potential at that point will be
A)
3V
B)
9V
C)
18V
D)
27V
1. The electric potential (V) at a distance (r) from a point charge (q) is given by the formula: V = k * q / r, where k is the electrostatic constant.
2. From this formula, we can see that the potential is inversely proportional to the distance (V ∝ 1/r).
3. Let the initial potential be V1 = 9 V and the initial distance be r1.
4. According to the problem, the new distance r2 = 3 * r1.
5. The new potential V2 can be calculated using the ratio: V2 / V1 = r1 / r2.
6. Substituting the values: V2 / 9 = r1 / (3 * r1) = 1/3.
7. Therefore, V2 = 9 / 3 = 3 V.
Comparing this to the options:
- Option (a) 3V is correct.
- Option (b) 9V would imply the distance didn't change.
- Option (c) 18V and (d) 27V would imply the distance decreased, which contradicts the problem statement.
The Q factor of a series RLC circuit increase if
A)
R increases
B)
R decreases
C)
applied voltage increases
D)
current decreases
The Quality factor (Q factor) of a series RLC circuit is a dimensionless parameter that describes how under-damped an oscillator is. It is defined as the ratio of the resonant frequency to the bandwidth, or more fundamentally, the ratio of the energy stored to the energy dissipated per cycle.
Mathematically, for a series RLC circuit, the Q factor is given by the formula:
Q = (1/R) * √(L/C)
From this formula, we can analyze the relationship between Q and the circuit components:
1. Resistance (R): Q is inversely proportional to R (Q ∝ 1/R). Therefore, if the resistance R decreases, the Q factor increases. Conversely, if R increases, the Q factor decreases.
2. Inductance (L) and Capacitance (C): Q increases if L increases or if C decreases.
Evaluating the options:
- Option (a) R increases: This would decrease the Q factor.
- Option (b) R decreases: This increases the Q factor (Correct).
- Option (c) applied voltage increases: The Q factor is a property of the circuit components (L, C, R) and is independent of the input voltage.
- Option (d) current decreases: The Q factor is a structural property of the circuit and does not depend on the instantaneous current flowing through it.
When an EM wave is incident from a more dense medium to less dense medium at an angle equal to or exceeding the critical angle, the wave suffers
A)
total internal transmission
B)
total internal reflection
C)
total internal refraction
D)
none of these
The phenomenon described in the question is a fundamental principle of optics and electromagnetic wave propagation.
1. **Conditions for Total Internal Reflection (TIR):** For TIR to occur, two conditions must be met:
- The wave must travel from an optically denser medium (higher refractive index, n1) to an optically rarer/less dense medium (lower refractive index, n2).
- The angle of incidence must be equal to or greater than the critical angle (θc).
2. **The Critical Angle:** The critical angle is the angle of incidence for which the angle of refraction is 90°. According to Snell's Law (n1 sin θ1 = n2 sin θ2), when θ2 = 90°, sin θc = n2/n1.
3. **What happens at or above the critical angle:**
- If the angle of incidence is exactly the critical angle, the refracted ray grazes the boundary.
- If the angle of incidence exceeds the critical angle, the wave cannot pass into the second medium (refraction is impossible) and is instead reflected entirely back into the denser medium.
4. **Evaluating Options:**
- (a) Total internal transmission: Incorrect; the wave is prevented from transmitting into the second medium.
- (b) Total internal reflection: Correct; this is the defined term for this phenomenon.
- (c) Total internal refraction: Incorrect; refraction refers to the bending of light as it passes from one medium to another; here, it fails to pass through.
- (d) None of these: Incorrect.
The purpose of choke in a fluorescent tube is
A)
to decrease the current
B)
to increase the current
C)
to decrease the voltage momentarily
D)
to increase the voltage momentarily
A fluorescent tube requires a high starting voltage to ionize the gas inside the tube and initiate the discharge process, but it requires a much lower voltage to maintain the arc once it has started. The 'choke' (which is an inductor) serves two primary purposes:
1. **Starting (Voltage Spike):** When the starter switch opens, the magnetic field in the choke collapses rapidly. According to Lenz's Law, this creates a high-voltage inductive kick (voltage spike) that is sufficient to ionize the gas in the tube, effectively increasing the voltage momentarily to start the lamp.
2. **Ballasting (Current Limiting):** Once the tube is conducting, it behaves like a negative resistance device. The choke then acts as a ballast to limit the current to a safe operating level to prevent the tube from drawing excessive current and burning out.
Comparing the options:
- Option (a) describes the 'ballast' function during steady-state operation, but the primary 'purpose' of the choke in the context of starting the tube is the voltage spike.
- Option (b) is incorrect as the choke limits current, it doesn't increase it.
- Option (c) is incorrect as decreasing voltage would prevent the tube from starting.
- Option (d) correctly identifies the inductive action required to strike the arc.