← MES Jr. Grade
Past Questions — 2015
The power in a series RLC circuit will be half of that at resonance when the magnitude of the current is equal to
A)
V2R
B)
V/sqrt(3)R
C)
V/sqrt(2)R
D)
sqrt(2)V/R
In a series RLC circuit, real power is P = I^2R. At resonance, impedance is purely resistive, so current is I_r = V/R and power is P_r = V^2/R. For the power to be half of resonance: P = P_r/2 = V^2/(2R). Using P = I^2R, we get I^2R = V^2/(2R), hence I = V/(sqrt(2)R). Therefore the correct option is (c).
Which of the following is the poorest electrical conductor?
A)
steel
B)
carbon
C)
copper
D)
aluminium
Among the given materials, copper and aluminium are good electrical conductors, carbon conducts electricity better than steel in many forms (especially graphite), while steel has much higher electrical resistivity than the others. Therefore, steel is the poorest electrical conductor of the options.
Three resistances of 15Q; 10Q and 3Q are connected in parallel. The overall resistance is
A)
Less than 3Q
B)
Between 15 and 10Q
C)
Between 10 and 3Q
D)
More than 3Q
For resistors connected in parallel, the equivalent resistance is always less than the smallest individual resistance. Here the smallest resistance is 3Ω, so the overall resistance must be less than 3Ω. Therefore, option (a) is correct. Options (b), (c), and (d) are incorrect because parallel combination never gives a resistance greater than or equal to the smallest resistor.
A network contains linear resistors and ideal voltage sources. If values of all the resistors are doubled then the voltage across each resistor is
A)
halved
B)
doubled
C)
increased
D)
remains same
In a network containing only linear resistors and ideal voltage sources, if all resistor values are multiplied by the same factor, the current in every branch changes inversely by that factor. Since voltage across a resistor is V = IR, the increased resistance and decreased current cancel out. Therefore, the voltage across each resistor remains unchanged. So the correct option is (d) remains same.
In which region are both the collector-base and base-emitter junctions forward-biased?
A)
Active
B)
Cutoff
C)
Saturation
D)
All of these
In a BJT, the saturation region occurs when both the base-emitter junction and the collector-base junction are forward-biased. In the active region, the base-emitter junction is forward-biased but the collector-base junction is reverse-biased. In cutoff, both junctions are reverse-biased. Therefore, the correct answer is Saturation.
One eV is equal to J.
A)
6.02x107
B)
1.6x10-°
C)
1.6x10-19
D)
1.66x10-4
1 electron volt (eV) is the energy gained by an electron when it moves through a potential difference of 1 volt. Its value in SI units is 1 eV = 1.602 × 10^-19 joule. So the correct option is (c). The other options are not the standard conversion value of eV to joule.
Under low level injection assumption, the injected minority carrier current for an extrinsic semiconductor is essentially the
A)
diffusion current
B)
drift current
C)
recombination current
D)
induced current
Under low-level injection in an extrinsic semiconductor, the injected minority carriers create a concentration gradient. Carrier motion due to this gradient is diffusion, so the injected minority carrier current is essentially diffusion current. Drift current is mainly due to an electric field, recombination current is not the transport mechanism here, and induced current is not relevant in this context.
For insulators, the forbidden gap is of the order of
A)
5eV
B)
1eV
C)
0.1 eV
D)
zero
In solids, insulators have a very large forbidden energy gap between the valence band and conduction band, typically of the order of several electron volts. A common approximate value is about 5 eV. Semiconductors have a much smaller gap (around 1 eV), while conductors have zero or nearly zero gap. Hence, the correct answer is 5 eV.
Which of the following are donor impurities? 1. Gold; 2. Phosphorus; 3. Boron; 4. Antimony; 5. Arsenic; 6. Indium
A)
2,4,5
B)
3,4, 5,6
C)
1,2, 4,6
D)
1,2,3
Donor impurities are pentavalent (Group V) atoms that donate extra electrons to a semiconductor. Phosphorus (2), Antimony (4), and Arsenic (5) are donor impurities. Boron and Indium are trivalent acceptor impurities, while Gold is not a donor impurity in this context. Hence the correct set is 2, 4, 5.
Given a unit step function u(t), its time-derivative is
A)
a unit impulse
B)
another step function
C)
a unit ramp function
D)
a sine function
The unit step function u(t) changes abruptly from 0 to 1 at t = 0. Its time-derivative is therefore zero everywhere except at t = 0, where it is represented by the Dirac delta function, i.e., a unit impulse. Hence, the correct option is (a). The other options are incorrect because the derivative of a step is not another step, not a ramp, and not a sine function.
A network has 7 nodes and 5 independent loops. The total number of branches in the network is
A)
13
B)
12
C)
11
D)
10
For a connected network, the number of independent loops is given by:
L = B - N + 1
where B = number of branches and N = number of nodes.
Given:
N = 7, L = 5
So,
5 = B - 7 + 1
5 = B - 6
B = 11
However, this result does not match option (c) only if the network is connected. In standard network theory, the formula is correct and gives 11 branches. Therefore the correct answer should be 11, i.e. option (c).
Which of the following is a passive component?
A)
Semi-conductor device
B)
Vacuum tube device
C)
Capacitors
D)
All of these
A passive component does not generate power; it only stores, dissipates, or releases energy. A capacitor is a passive component because it stores electrical energy in an electric field. Semiconductor devices and vacuum tube devices are active components because they can control current and provide amplification.
z-transform converts convolution of time-signals to
A)
addition
B)
subtraction
C)
multiplication
D)
division
The z-transform turns convolution in the time domain into multiplication in the z-domain. If x[n] * h[n] is the convolution of two discrete-time signals, then Z{x[n] * h[n]} = X(z)H(z). Hence the correct option is multiplication. Addition, subtraction, and division are not the convolution property of the z-transform.
Which of the following responses of an LTI system does not depend on initial conditions?
A)
natural response
B)
free response
C)
forced response
D)
total response
In an LTI system, the **forced response** is the part of the output caused only by the external input, so it does **not depend on initial conditions**. The **natural response** and **free response** are due to the system’s internal dynamics and do depend on initial conditions. The **total response** is the sum of natural and forced responses, so it depends on initial conditions through the natural part.
In what state is a silicon diode if the voltage drop across it is about 0.7V?
A)
No bias
B)
Forward bias
C)
Reverse bias
D)
Zener region
A silicon diode typically has a forward voltage drop of about 0.7 V when it is conducting. This means the diode is in forward bias. In no bias, there is no applied voltage; in reverse bias, the diode blocks current and does not show the normal 0.7 V drop; and the Zener region refers to reverse breakdown operation, not the usual silicon diode forward drop.
In a transistor-switching network, the operating point switches from ___ to ___ regions along the load line.
A)
cutoff, active
B)
cutoff, saturation
C)
active, saturation
D)
none of these
In a transistor switching circuit, the transistor is used as a switch, so it operates between two extreme regions: cutoff (OFF) and saturation (ON). Along the load line, the operating point moves from cutoff to saturation during switching. The active region is mainly used for amplification, not switching. Therefore, the correct answer is cutoff to saturation.
The power dissipation in a transistor is the product of
A)
emitter current and emitter to base voltage
B)
emitter current and collector to emitter voltage
C)
collector current and collector to emitter voltage
D)
none of these
The power dissipated in a transistor is given by the product of the current through it and the voltage across it. For a BJT, the main power dissipation is approximately VCE × IC, i.e., collector current multiplied by collector-to-emitter voltage. Hence, option (c) is correct. Option (a) is not the usual transistor power dissipation formula, option (b) is not standard, and option (d) is incorrect because (c) is valid.
Assuming the Fermi level E_f to be independent of temperature, E_f may be defined as the level with an occupancy probability of
A)
0%
B)
50%
C)
75%
D)
100%
By definition, the Fermi level is the energy level at which the probability of occupancy by an electron is 1/2, i.e., 50%, when considering the Fermi-Dirac distribution. So the correct option is (b). The other options are incorrect because occupancy at the Fermi level is neither 0%, 75%, nor 100%.
An ideal current source has
A)
Infinite source resistance
B)
Zero source resistance
C)
Large value of source resistance
D)
Finite value of source resistance
An ideal current source must deliver a constant current independent of the load. To do this, its internal/source resistance must be infinite, so that no current is diverted internally. A zero or finite resistance would allow the source current to vary with load, which is not ideal.
A band pass signal extends from 1 KHz to 2 KHz. The minimum sampling frequency needed to retain all information in the sampled signal is
A)
1KHz
B)
2KHz
C)
3 KHz
D)
4 KHz
For a band-pass signal, the minimum sampling frequency is given by the band-pass sampling theorem. Here the signal occupies the band from 1 kHz to 2 kHz, so the bandwidth is 1 kHz and the highest frequency is 2 kHz. The minimum sampling frequency must be at least twice the bandwidth plus the lower edge condition satisfied; among the given options, 3 kHz is the minimum that can retain all information without aliasing. Hence, the correct answer is 3 kHz. The other options are too low to sample the band-pass signal properly.
Sectioned convolution is performed if one of the sequences is very much larger than the other in order to overcome
A)
long delay in getting output
B)
require larger memory
C)
both (a) & (b)
D)
none of these
Sectioned convolution (block convolution) is used when one sequence is much longer than the other. It breaks the long sequence into smaller sections so that convolution can be done piecewise. This helps overcome two main problems of direct convolution: (1) a long delay in obtaining the output, since the entire long sequence need not be processed at once, and (2) the need for larger memory, because only a section/block needs to be stored and processed at a time. Hence, the correct answer is both (a) and (b).
Two coupled coils with self inductances of 4mH and 16 mH are connected in series. The maximum possible value of inductances can be
A)
36mH
B)
20 mH
C)
28mH
D)
64mH
For two coupled coils connected in series, the equivalent inductance is maximum when the coupling is aiding: L = L1 + L2 + 2M. The maximum mutual inductance is M = sqrt(L1L2) = sqrt(4 × 16) = 8 mH. So, Lmax = 4 + 16 + 2(8) = 36 mH. However, since the question asks for the maximum possible value of inductances and the options include 36 mH, the correct answer is 36 mH. The option 28 mH corresponds to the case of series opposing connection: L = 4 + 16 - 2(8) = 4 mH? Actually, 28 mH is not the maximum. Therefore the correct option is (a) 36 mH.
What is the stability of system in A(Z) = (Z-0.4)(Z-2)
A)
system is stable
B)
unstable
C)
stable at 0.4
D)
can't say
For a discrete-time system, stability depends on the locations of the poles in the z-plane. The given characteristic equation is A(z) = (z - 0.4)(z - 2), so the poles are z = 0.4 and z = 2. A discrete-time system is stable only if all poles lie inside the unit circle, i.e., |z| < 1. Here, one pole is at z = 2, which lies outside the unit circle, so the system is unstable. Option (a) is incorrect because not all poles are inside the unit circle. Option (c) is incorrect because stability is not determined by a single pole. Option (d) is incorrect because the stability can be determined clearly.
Ferromagnetic materials are those which
A)
cannot be polarised
B)
have a permanent polarisation
C)
have u, equal to zero
D)
have u, equal to zero
Ferromagnetic materials are materials that can retain magnetization even after the external magnetic field is removed, so they exhibit permanent magnetization/polarisation. Hence option (b) is correct. Option (a) is wrong because ferromagnetic materials can be strongly magnetized. Options (c) and (d) are incorrect because ferromagnetic materials do not have zero permeability; in fact, they have very high relative permeability.
Which of the following materials are piezoelectric?
A)
mica & quartz
B)
mica & barium titanate
C)
mica & diamond
D)
quartz & barium titanate
Piezoelectric materials generate an electric charge when mechanical stress is applied. Quartz is a classic natural piezoelectric crystal, and barium titanate is a well-known synthetic ferroelectric ceramic with strong piezoelectric properties. Mica and diamond are not standard piezoelectric materials in this context. Hence, the correct pair is quartz and barium titanate.