← MES Jr. Grade
Past Questions — 2022
Superposition theorem is not applicable for :
A)
Voltage calculations
B)
Bilateral elements
C)
Passive elements
D)
Power calculations
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.
1. **Linearity Requirement**: The theorem relies on the principle of linearity. Voltage and current are linear functions of the source values. Therefore, it is perfectly applicable for voltage and current calculations (making option 'a' incorrect).
2. **Bilateral and Passive Elements**: The theorem is designed for linear bilateral networks (networks where the properties of elements do not change with the direction of current) and passive elements like resistors, capacitors, and inductors (making options 'b' and 'c' incorrect).
3. **Power Calculations**: Power is a non-linear quantity because it is proportional to the square of the current or voltage (P = I²R or P = V²/R). Because the relationship is quadratic rather than linear, the total power is NOT the sum of the powers calculated from individual sources. For example, if two sources produce currents I1 and I2, the total power is (I1 + I2)²R, which is not equal to I1²R + I2²R. Thus, superposition cannot be applied directly to power calculations.
Describe the Hall Effect and explain its relation to mechanical force exerted by magnetic field on conduction.
In a MOSFET operating in the saturation region, the channel length modulation effect causes :
A)
An increase in the gate – source capacitance
B)
A decrease in the transconductance
C)
A decrease in the unity – gain cut – off frequency
D)
A decrease in the output resistance
A decrease in the output resistance is the best answer because it directly satisfies the fact, principle, or condition asked in the question.
A hall effect transducer can be used to measure :
A)
Displacement, position and velocity
B)
Displacement, temperature and magnetic flux
C)
Position, pressure and velocity
D)
Energy
The Hall Effect occurs when a current-carrying conductor is placed in a magnetic field, resulting in a transverse voltage (Hall voltage) proportional to the magnetic field strength and the current.
1. **Position and Displacement**: By placing a permanent magnet on a moving object and a Hall sensor at a fixed location, the change in magnetic flux density as the object moves allows for the precise measurement of position and linear or angular displacement.
2. **Velocity**: Hall effect sensors are widely used in tachometers and speed sensors. By counting the frequency of pulses generated as a toothed ferromagnetic wheel (attached to a rotating shaft) passes the sensor, the rotational velocity can be calculated.
Evaluating other options:
- Option (b) is incorrect because Hall effect sensors are not primary transducers for temperature measurement (though they are temperature-sensitive, this is usually an error to be compensated for, not the intended measurement).
- Option (c) is incorrect because Hall effect sensors do not directly measure pressure (unless coupled with a diaphragm and a magnet, but it is not a standard direct application like position/velocity).
- Option (d) is incorrect as energy is a scalar quantity derived from power over time, not something measured directly by a Hall transducer.
What is the difference between active and passive devices? Why it is necessary to connect an electrolytic capacitor in a circuit with correct polarity?
Explain the working of Zener diode as a shunt regulator.
The Fourier transform of a conjugate symmetric function is always :
A)
Imaginary
B)
Conjugate antisymmetric
C)
Real
D)
Conjugate symmetric
A function x(t) is said to be conjugate symmetric if it satisfies the condition x(t) = x*(-t), where * denotes the complex conjugate.
According to the properties of the Fourier Transform, if a signal x(t) is conjugate symmetric, its Fourier Transform X(ω) is purely real.
Mathematical Proof:
1. The Fourier Transform is defined as X(ω) = ∫ x(t) e^(-jωt) dt.
2. If x(t) = x*(-t), then X(ω) = ∫ x*(-t) e^(-jωt) dt.
3. Let u = -t, then dt = -du. The limits change from (-∞, ∞) to (∞, -∞).
4. X(ω) = ∫ x*(u) e^(jωu) du.
5. Notice that the expression ∫ x*(u) e^(jωu) du is exactly the complex conjugate of the Fourier Transform formula: X*(ω) = ∫ x*(t) e^(jωt) dt.
6. Therefore, X(ω) = X*(ω).
7. Any complex number that is equal to its own conjugate must be purely real.
Analysis of options:
- (a) Imaginary: This occurs if the function is conjugate antisymmetric (x(t) = -x*(-t)).
- (b) Conjugate antisymmetric: This is a property of the signal, not the result of the transform in this context.
- (c) Real: Correct, as proven above.
- (d) Conjugate symmetric: This is the property of the input signal, not necessarily the resulting transform.
When copper is added to silver in small quantity so as to form an alloy, the resistivity of such an alloy is:
A)
Equal to the resistivity of the copper
B)
Equal to the resistivity of the silver
C)
Greater than the resistivity of the copper
D)
In between the resistivity of copper and silver
This question relates to the physics of electrical resistivity in alloys. Silver (Ag) is the most conductive element (lowest resistivity), and Copper (Cu) is the second most conductive element. When a solute (like copper) is added to a solvent (like silver) to form a solid solution alloy, the resistivity of the resulting alloy increases significantly compared to both pure components. This is due to 'impurity scattering' or 'alloy scattering.' In a pure metal, electrons move through a periodic lattice with minimal scattering. Adding atoms of a different element (even if that element is also a good conductor) disrupts the periodicity of the crystal lattice. These lattice distortions act as scattering centers for conduction electrons, increasing the mean free path's resistance. Therefore, the resistivity of a silver-copper alloy is higher than that of pure silver and also higher than that of pure copper, regardless of the fact that both constituents are highly conductive. This is a general rule in material science: alloying typically increases the electrical resistivity of a metal.
If all the elements in a particular network are linear then the superposition theorem holds when the excitation is :
A)
dc only
B)
ac only
C)
either ac or dc
D)
an impulse
The Superposition Theorem states that in any 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 Requirement**: The fundamental prerequisite for the superposition theorem is that the network must be linear. A linear network is one where the parameters (Resistance, Inductance, Capacitance) do not change with the change in voltage or current.
2. **Nature of Excitation**: Linearity is a property of the network components, not the source. Whether the excitation is a constant Direct Current (DC), a sinusoidal Alternating Current (AC), or a combination of both, the principle of linearity (additivity and homogeneity) remains valid.
3. **Application**: If a circuit has both DC and AC sources, the total response is the sum of the DC response (calculated by treating capacitors as open circuits and inductors as short circuits) and the AC response (calculated using phasors/impedances).
Therefore, the theorem holds regardless of whether the excitation is AC, DC, or a mix of both.
Transient current of an RLC circuit is oscillatory when :
A)
R = 2 sqrt(L/C)
B)
R < 2 sqrt(L/C)
C)
R = 0
D)
R > 2 sqrt(L/C)
In a series RLC circuit, the behavior of the transient current is determined by the roots of the characteristic equation: s^2 + (R/L)s + (1/LC) = 0. The roots are given by s = -α ± √(α² - ω₀²), where α = R/(2L) is the damping coefficient and ω₀ = 1/√LC is the undamped natural frequency.
1. Underdamped (Oscillatory): This occurs when the term under the square root is negative (α² < ω₀²). This leads to complex conjugate roots, resulting in a sinusoidal response that decays exponentially over time.
Condition: (R/2L)² < 1/LC
R²/4L² < 1/LC
R² < 4L/C
R < 2√(L/C).
2. Critically Damped: This occurs when α² = ω₀², meaning R = 2√(L/C). The system returns to equilibrium as quickly as possible without oscillating.
3. Overdamped: This occurs when α² > ω₀², meaning R > 2√(L/C). The system returns to equilibrium slowly without oscillating.
Therefore, for the transient current to be oscillatory, the circuit must be underdamped, which requires R < 2√(L/C).
For maximum power transfer between two cascaded sections of an electrical network, the relationship between the output impedance Z1 of the first section to the input impedance Z2 of the second section is:
A)
Z1 = Z2
B)
Z1 = - Z2
C)
Z1 = Z2*
D)
Z1 = - Z2*
The Maximum Power Transfer Theorem states that to transfer the maximum amount of power from a source network to a load network, the load impedance must be the complex conjugate of the source impedance. In the context of two cascaded sections, the first section acts as the source with an output impedance Z1, and the second section acts as the load with an input impedance Z2. For maximum power transfer, the condition is Z2 = Z1*, which is mathematically equivalent to Z1 = Z2* (since the conjugate of a conjugate is the original value).
Breaking down the options:
- Option (a) Z1 = Z2: This is only true for purely resistive circuits. In AC circuits with reactance, this does not maximize power transfer because it doesn't cancel out the reactive components.
- Option (b) Z1 = -Z2: This is physically unrealistic for passive networks as it implies negative resistance/reactance.
- Option (c) Z1 = Z2*: This is the correct complex conjugate match. If Z1 = R1 + jX1 and Z2 = R2 + jX2, then for maximum power, R1 = R2 and X1 = -X2. This ensures that the total reactance of the combined circuit is zero (resonance), allowing maximum current to flow and maximum power to be dissipated in the load.
- Option (d) Z1 = -Z2*: This does not satisfy the condition for maximum power transfer.
The Early – Effect in a bipolar junction transistor is caused by :
A)
Fast – turn – on.
B)
Fast – turn – off.
C)
Large collector – base reverse bias.
D)
Large emitter – base forward bias.
The Early Effect, also known as Base-Width Modulation, occurs in a Bipolar Junction Transistor (BJT) when the reverse bias voltage across the collector-base (CB) junction is increased.
1. **Mechanism**: In a BJT, the collector-base junction is reverse-biased. As the reverse bias voltage ($V_{CB}$) increases, the depletion region at this junction widens.
2. **Base-Width Modulation**: Because the depletion region extends into the base (especially in lightly doped bases), the effective width of the neutral base region decreases.
3. **Impact**: A narrower base leads to a higher concentration gradient of minority carriers across the base, which increases the collector current ($I_C$) even if the emitter-base voltage ($V_{BE}$) remains constant. This results in a finite output resistance rather than an ideal infinite resistance in the active region.
**Analysis of Options:**
- **Option a & b**: Fast turn-on/off relate to switching speeds and parasitic capacitances, not the steady-state base-width modulation known as the Early Effect.
- **Option d**: Forward bias at the emitter-base junction is necessary for the transistor to operate in the active region, but it does not cause the modulation of the base width associated with the Early Effect; that is specifically driven by the CB junction bias.
A discrete time system is stable if all the roots of the characteristics equation lie :
A)
Outside the circle of unit radius
B)
Within the circle of unit radius
C)
Outside the circle of radius equal to 3-units
D)
On the circle of infinite radius.
In the analysis of discrete-time systems, stability is determined by the location of the poles of the system's transfer function (which are the roots of the characteristic equation) in the z-plane.
1. **The z-Transform and Stability**: For a causal discrete-time system to be Bounded-Input Bounded-Output (BIBO) stable, the region of convergence (ROC) of the transfer function must include the unit circle (|z| = 1).
2. **Pole Location**: For a causal system, the ROC is the exterior of a circle centered at the origin with a radius equal to the magnitude of the outermost pole. Therefore, for the ROC to include the unit circle, all poles (roots of the characteristic equation) must lie strictly inside the unit circle (|z| < 1).
3. **Analysis of Options**:
- **Option (a)**: If poles are outside the unit circle, the system is unstable because the impulse response will grow exponentially.
- **Option (b)**: This is the correct condition. All roots must be within the unit circle (|z| < 1) for stability.
- **Option (c)**: A radius of 3 units is arbitrary and does not define the stability boundary for general discrete systems.
- **Option (d)**: A circle of infinite radius is not a valid boundary for stability analysis.
The tree branches of a graph are called :
A)
chords
B)
links
C)
twigs
D)
co-tree
In network topology and graph theory, a 'tree' is a connected subgraph that contains all the nodes of the original graph but contains no closed loops (cycles).
1. **Links (or Twigs):** The branches that form the tree are called 'links' (or sometimes 'twigs'). If a graph has 'n' nodes, the tree will always consist of exactly 'n-1' links.
2. **Chords:** The branches of the original graph that are NOT part of the tree are called 'chords' (or links of the co-tree).
3. **Co-tree:** The set of all chords in a graph is referred to as the 'co-tree'.
While 'twigs' is sometimes used as a synonym for links in specific textbooks, 'links' is the standard technical term used in most electrical network analysis and graph theory contexts for the branches of a tree. Therefore, option (b) is the most accurate and standard answer.
The silicon transistor are more widely used than germanium transistors because :
A)
they have smaller leakage current
B)
they have better ability to dissipate heat
C)
they have smaller depletion layer
D)
they have larger current carrying capacity
The primary reason silicon (Si) transistors are preferred over germanium (Ge) transistors is their significantly lower reverse saturation current (leakage current). This is due to the wider energy bandgap of silicon (~1.1 eV) compared to germanium (~0.67 eV). A wider bandgap means that fewer electrons can thermally jump from the valence band to the conduction band at room temperature, resulting in a much smaller minority carrier concentration and thus a lower leakage current (I_CBO). This makes silicon devices more stable, especially at higher temperatures.
Evaluating other options:
- Option b: While silicon devices are often packaged better, the material property of heat dissipation is not the primary reason for the shift from Ge to Si; in fact, Ge has higher carrier mobility.
- Option c: The depletion layer width depends on doping levels and applied voltage, not inherently on the material being Si or Ge in a way that makes Si 'better'.
- Option d: Current carrying capacity is primarily determined by the physical size and doping of the device, not the intrinsic material choice between Si and Ge.
An intrinsic semiconductor at absolute zero temperature behaves like :
A)
An electron
B)
An insulator
C)
A conductor
D)
An ion
Step-by-step reasoning: 1. An intrinsic semiconductor is a pure semiconductor (like Silicon or Germanium) without any intentional impurities. 2. In a semiconductor, there is a small energy gap (band gap) between the valence band (where electrons are bound to atoms) and the conduction band (where electrons are free to move and conduct electricity). 3. At absolute zero temperature (0 Kelvin), the thermal energy available to the electrons is zero. 4. Because there is no thermal energy to excite electrons from the valence band across the band gap into the conduction band, the conduction band remains completely empty and the valence band remains completely full. 5. Since there are no free charge carriers (electrons or holes) available to move through the crystal lattice, the material cannot conduct electricity. Therefore, it behaves as a perfect insulator.
Why other options are incorrect:
- (a) An electron is a subatomic particle, not a material behavior.
- (c) A conductor requires a high density of free charge carriers, which are absent at 0K in an intrinsic semiconductor.
- (d) An ion is a charged atom/molecule; the semiconductor remains a neutral crystal lattice.
When the gate – to – source voltage (VGS) of a MOSFET with threshold voltage of 400 mV, working in saturation is 900 mV, the drain current is observed to be 1 mA. Neglecting the channel width modulation effect and assuming that the MOSFET is operating at saturation, the drain current for an applied VGS of 1400 mV is :
A)
0.5 mA
B)
2.0 mA
C)
3.5 mA
D)
4.0 mA
4.0 mA is the best answer because it directly satisfies the fact, principle, or condition asked in the question.
Determine the inverse Laplace transform of X(s) = 1 / ((s+2)(s^2 + s + 1)).
The impurity commonly used for realizing the base region of a silicon n-p-n transistor is :
A)
Phosphorus
B)
Gallium
C)
Boron
D)
Indium
1. Analysis of the Transistor Type: The question specifies an n-p-n transistor. In an n-p-n transistor, the emitter and collector are n-type regions, and the base is a p-type region.
2. Doping Requirements: To create a p-type region in silicon (a Group IV element), the silicon must be doped with a trivalent impurity (Group III element), which creates 'holes' as the majority charge carriers.
3. Evaluating the Options:
- Phosphorus (Option a): A Group V element. It provides extra electrons, making the silicon n-type. Therefore, it is used for the emitter and collector, not the base of an n-p-n transistor.
- Gallium (Option b): A Group III element. While it can create p-type silicon, it is less commonly used than Boron for standard transistor fabrication due to its diffusion characteristics.
- Boron (Option c): A Group III element. It is the most common and standard p-type dopant used in the semiconductor industry for silicon-based devices because of its ideal atomic size and diffusion properties.
- Indium (Option d): A Group III element. Like Gallium, it can create p-type silicon, but it is rarely used as the primary dopant for the base region in standard BJT fabrication.
4. Conclusion: Boron is the industry-standard impurity used to realize the p-type base region of a silicon n-p-n transistor.
For the network shown in the figure below, obtain branch voltages using KCL equations on node basis.
The system is defined by its impulse h(n) = e^n u(n-2) is :
A)
Unstable and anti-causal
B)
Unstable and causal
C)
Stable and Causal
D)
Stable and non-causal
To determine the properties of the system, we analyze the given impulse response: h(n) = e^n u(n-2).
1. **Causality**: A discrete-time system is causal if its impulse response h(n) = 0 for n < 0.
The term u(n-2) is the unit step function shifted by 2. It is defined as:
u(n-2) = 1 for n ≥ 2
u(n-2) = 0 for n < 2
Since h(n) = 0 for all n < 0 (specifically, it is zero for n < 2), the system is **Causal**.
2. **Stability**: A discrete-time LTI system is BIBO (Bounded-Input Bounded-Output) stable if its impulse response is absolutely summable, i.e., Σ |h(n)| < ∞.
Let's evaluate the sum:
Σ_{n=-∞}^{∞} |e^n u(n-2)| = Σ_{n=2}^{∞} e^n
This is a geometric series with the first term a = e^2 and common ratio r = e.
Since the common ratio r = e ≈ 2.718, which is greater than 1, the series diverges to infinity.
Because the sum is not finite, the system is **Unstable**.
Conclusion: The system is Unstable and Causal.
The frequency spectrum indicates :
A)
The relative phase of each frequency component
B)
The relative magnitude of each frequency component
C)
The relative frequency of each frequency component
D)
None of these
In signals and systems, a frequency spectrum is a representation of a signal in the frequency domain (typically obtained via the Fourier Transform). A signal is decomposed into its constituent sinusoidal components. The frequency spectrum specifically refers to the plot of the magnitude (amplitude) of these components against their respective frequencies. While a complete Fourier Transform provides both magnitude and phase, the term 'frequency spectrum' (or magnitude spectrum) is primarily used to describe how the energy or power of the signal is distributed across different frequencies, thus indicating the relative magnitude of each frequency component. Option (a) refers to the phase spectrum, and option (c) is redundant as frequency is the independent variable (the x-axis), not the value being indicated by the spectrum's height.
What is photo diode? With proper characteristics curves and relevant diagrams explain the operation of photo diode. Explain the concept of photo conductivity.
An avalanche photo diode is operated under :
A)
Small forward bias
B)
Small reverse bias
C)
Independent of bias
D)
Large reverse bias
An Avalanche Photo Diode (APD) is a highly sensitive photodetector designed to provide internal gain. To achieve this gain, the diode must be operated under a large reverse bias voltage. When a high reverse bias is applied, a strong electric field is created within the depletion region. When a photon is absorbed and creates an electron-hole pair, these carriers are accelerated by the intense electric field to very high kinetic energies. These high-energy carriers collide with the crystal lattice, knocking more electrons out of the valence band and creating additional electron-hole pairs. This process is known as 'impact ionization,' leading to an 'avalanche' effect that multiplies the initial photocurrent.
Why other options are incorrect:
- (a) Small forward bias: Forward biasing allows current to flow easily and would saturate the diode, preventing the detection of light-induced carriers.
- (b) Small reverse bias: While a standard PIN photodiode operates under reverse bias, a 'small' reverse bias is insufficient to trigger the impact ionization required for the avalanche effect.
- (c) Independent of bias: The operation of an APD is strictly dependent on the bias voltage to create the necessary electric field for carrier multiplication.
When the diode is forward biased, it is equivalent to :
A)
An off switch
B)
An On switch
C)
A high resistance
D)
A low resistance
A diode is a semiconductor device that allows current to flow in only one direction.
1. **Forward Bias Condition**: When the positive terminal of a voltage source is connected to the P-type material (anode) and the negative terminal to the N-type material (cathode), the diode is said to be forward biased.
2. **Mechanism**: In forward bias, the external voltage overcomes the internal barrier potential (approximately 0.7V for Silicon). This narrows the depletion region, allowing majority charge carriers to flow across the junction.
3. **Equivalent Circuit**: In an ideal model, a forward-biased diode acts as a closed switch (an 'On' switch) with zero resistance, allowing current to flow freely. In a practical model, it acts as a small voltage source in series with a very low resistance.
**Analysis of other options:**
- **Option a (An off switch):** This describes a diode in reverse bias, where it blocks current flow.
- **Option c (A high resistance):** This is characteristic of a reverse-biased diode.
- **Option d (A low resistance):** While a forward-biased diode does have low resistance, the term 'On switch' is the standard conceptual equivalent used in circuit analysis to describe the state of conduction.