← MES Jr. Grade
Past Questions
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).
The dual of a parallel R-C circuit is a :
A)
Series R-C circuit
B)
Series R-L circuit
C)
Parallel R-C circuit
D)
Parallel R-C circuit
In network theory, the concept of duality allows us to transform one circuit into another by replacing specific elements and parameters while maintaining the same mathematical form of the governing equations. The duality rules are as follows:
1. **Topology Transformation**: A parallel connection becomes a series connection, and vice versa.
2. **Element Transformation**:
- Resistance (R) $\leftrightarrow$ Conductance (G). Since both are resistive elements, R remains R (or transforms to G, which is still a resistive component).
- Capacitance (C) $\leftrightarrow$ Inductance (L). This is because the voltage-current relationship for a capacitor is $i = C \frac{dv}{dt}$ and for an inductor is $v = L \frac{di}{dt}$.
3. **Parameter Transformation**: Voltage $\leftrightarrow$ Current, and Mesh $\leftrightarrow$ Node.
Applying these rules to a 'Parallel R-C circuit':
- 'Parallel' becomes 'Series'.
- 'R' (Resistor) remains a resistive element 'R'.
- 'C' (Capacitor) becomes 'L' (Inductor).
Therefore, the dual of a parallel R-C circuit is a series R-L circuit.
Which of the following is not associated with P-N junction?
A)
Junction capacitance
B)
Charge storage capacitance
C)
Depletion capacitance
D)
Channel length modulation
To determine which option is not associated with a P-N junction, let's analyze each term:
1. **Junction Capacitance (a):** This is a general term referring to the capacitance that occurs at the P-N junction. It is composed of both depletion capacitance and diffusion (charge storage) capacitance.
2. **Charge Storage Capacitance (b):** Also known as Diffusion Capacitance, this occurs when a P-N junction is forward-biased. Minority carriers are injected across the junction and stored in the neutral regions, creating a capacitance effect.
3. **Depletion Capacitance (c):** Also known as Transition Capacitance, this occurs when a P-N junction is reverse-biased. The depletion region acts as a dielectric between the P and N regions (which act as conducting plates), creating a capacitor.
4. **Channel Length Modulation (d):** This is a phenomenon specifically associated with **Field Effect Transistors (FETs)**, such as MOSFETs. It occurs when the drain-source voltage ($V_{DS}$) increases beyond the saturation point, causing the effective length of the conducting channel to decrease, which in turn increases the drain current. It is a property of a three-terminal device with a channel, not a basic two-terminal P-N junction.
Therefore, channel length modulation is the only option not associated with a P-N junction.
In a p-channel JFET, the charge carriers are :
A)
Electrons
B)
Holes
C)
Both electrons and holes
D)
Atom
A Junction Field Effect Transistor (JFET) is a unipolar device, meaning the current is carried by only one type of charge carrier. The type of carrier depends on the material used for the conducting channel:
1. In an n-channel JFET, the channel is made of n-type semiconductor material, and the majority charge carriers are electrons.
2. In a p-channel JFET, the channel is made of p-type semiconductor material. In p-type materials, the majority charge carriers are holes.
Since the question specifically asks about a p-channel JFET, the charge carriers are holes.
Analysis of other options:
- Option (a) Electrons: These are the carriers for n-channel JFETs.
- Option (c) Both electrons and holes: This describes bipolar devices (like BJTs), not unipolar devices like JFETs.
- Option (d) Atom: Atoms are neutral particles and do not act as charge carriers for electrical current in semiconductors.
Find the Y parameters
The convolution of x(t) and h(t) is given by y(t) = integral from -infinity to infinity of x(tau)h(t-tau), then :
A)
Both x(t) and h(t) are causal
B)
Both x(t) and h(t) are non-causal
C)
x(t) is causal and h(t) is non-causal
D)
x(t) is non-causal and h(t) is causal
1. **Definition of Convolution**: The general formula for the convolution of two continuous-time signals $x(t)$ and $h(t)$ is given by $y(t) = \int_{-\infty}^{\infty} x(\tau)h(t-\tau) d\tau$. This is the standard mathematical definition and applies regardless of whether the signals are causal or non-causal.
2. **Definition of Causality**: A signal is said to be causal if it is zero for all $t < 0$. For a system to be causal, its impulse response $h(t)$ must be causal ($h(t) = 0$ for $t < 0$).
3. **Analysis of the Integral Limits**: In practical engineering and competitive exam contexts for 'Signals and Systems', when the convolution integral is presented in its general form, the question often tests the condition under which the integral simplifies or the physical realization of the system.
4. **Evaluating the Options**:
- If $x(t)$ and $h(t)$ are both causal, the limits of integration effectively change from $(-\infty, \infty)$ to $(0, t)$. This is because $x(\tau) = 0$ for $\tau < 0$ and $h(t-\tau) = 0$ for $t-\tau < 0$ (which means $\tau > t$).
- While the general formula provided in the question is mathematically true for *any* two signals, in the context of standard textbook problems for this specific exam pattern, the expression $y(t) = \int_{-\infty}^{\infty} x(\tau)h(t-\tau) d\tau$ is the fundamental definition used to derive the output of a Linear Time-Invariant (LTI) system.
- For a system to be physically realizable (causal), the impulse response $h(t)$ must be causal. If the input $x(t)$ is also causal (starts at $t=0$), the convolution represents a real-time process.
5. **Conclusion**: Given the options provided, the question asks for the condition associated with this operation in a standard LTI system context. The most appropriate answer in the context of engineering causality is that both the input and the impulse response are causal, allowing the system to operate in real-time.
A certain series resonant circuit has a bandwidth of 1000 Hz. If the existing coil is replaced by a coil with low Q, what happens to the bandwidth?
A)
Bandwidth will increase
B)
Bandwidth becomes zero
C)
Bandwidth will decrease
D)
Bandwidth remains the same
In a series resonant circuit, the relationship between the resonant frequency (f₀), the Quality factor (Q), and the Bandwidth (BW) is given by the formula: BW = f₀ / Q.
1. **Understanding Q (Quality Factor):** The Q factor represents the sharpness of the resonance. For a series RLC circuit, Q = (ω₀L) / R. A 'low Q' coil typically implies a higher internal resistance (R) relative to its inductance (L).
2. **Analyzing the Relationship:** From the formula BW = f₀ / Q, it is evident that the bandwidth is inversely proportional to the Quality factor (BW ∝ 1/Q).
3. **Effect of replacing the coil:** If the existing coil is replaced by one with a lower Q, the denominator in the bandwidth equation decreases.
4. **Conclusion:** As Q decreases, the Bandwidth (BW) must increase. This means the resonance curve becomes flatter and wider, allowing a broader range of frequencies to pass through the circuit.
Therefore, option (a) is correct. Option (c) is incorrect because that would happen if Q increased. Option (b) is physically impossible for a passive circuit, and option (d) is incorrect because BW depends directly on the Q of the components used.
Explain the working of Zener diode as a shunt regulator.
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.
Find the voltage across the 5W resistor in the figure given below by using Superposition theorem.
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.
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.
With the help of energy band diagram, distinguish between insulators, conductors and semiconductors.
What is the difference between active and passive devices? Why it is necessary to connect an electrolytic capacitor in a circuit with correct polarity?
Describe the Hall Effect and explain its relation to mechanical force exerted by magnetic field on conduction.
For the network shown in the figure below, obtain branch voltages using KCL equations on node basis.
Determine the inverse Laplace transform of X(s) = 1 / ((s+2)(s^2 + s + 1)).
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.
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.
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.
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.
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.
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.
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.