Thursday, February 13, 2014

Multiple Choice Questions on Semiconductor Electronics



“Man perfected by society is the best of all animals; he is the most terrible of all when he lives without law and without justice.”
– Aristotle



Questions on semiconductor electronics are generally simple and you can answer most of the questions correctly without consuming much time. But you need to understand the simple fundamental principles of operation of various semiconductor devices so that common mistakes are avoided.

Here are a few multiple choice questions involving semiconductor electronics:

(1) A square wave of peak to peak voltage 100 volt is applied between the input terminals A and B of the circuit shown in the adjoining figure. What is the voltage across the capacitor C?
(a) 100 V
(b) 0 V
(c) 50 V
(d) 100√2 V
(e) 50√2 V
The diode will pass only the negative half cycles of the square voltage wave so that the voltage across the capacitor will be 50 V.
(2) If a sine wave of peak to peak voltage 100 volt is applied between the input terminals A and B of the circuit shown in the above question, what will be the voltage across the capacitor C?
(a) 100√2 V
(b) 50√2 V
(c) 50 V
(d) 100 V
(e) 0 V
In this case also the diode will pass only the negative half cycles of the applied voltage wave. Even though the voltage varies during the half cycle, the capacitor can retain the charge on it so that the voltage across the capacitor will be 50 V itself.
(3) If a 230 volt house supply alternating voltage is applied between the terminals A and B of the circuit shown in Question No. 1, what will be the voltage across the capacitor C?
(a) 230√2 V
(b) 115√2 V
(c) 230 V
(d) 150 V
(e) 0 V
Alternating voltages and alternating currents (A.C.) supplied to houses are specified in terms of root mean square (RMS) values. Thus a specified value of 230 volt a.c. means that the root mean square value of the voltage is 230 V. Therefore, the peak value of the alternating voltage is 230√2 V.
The diode will conduct during negative half cycles only and the capacitor will be charged to the peak value of the applied voltage. Assuming that the capacitor is ideal, the charge will be retained through out the entire cycle of the applied voltage so that the voltage across the capacitor will be 230√2 V.

(4) The truth table for the digital circuit shown in the figure above is



When both A and B are zero, the NAND gate on the input side produces an input at level 1 for the NOR gate on the output side. Therefore, the final output Y = 0.
When A = 0 and B = 1, the NAND gate on the input side again produces an input at level 1 for the NOR gate on the output side. In this case also the final output Y = 0.
When A = 1 and B = 0, the NAND gate on the input side once again produces an input at level 1 for the NOR gate on the output side. Once again the final output Y = 0.
When both A and B are at level 1, the NAND gate on the input side produces an input at level 0 for the NOR gate on the output side.
The inverter connected to the other input of  the NOR gate also supplies an input at level 0 for the NOR gate on the output side. Since both inputs of the NOR gate are at zero level, its output Y = 1.
The correct truth table is (b).

(5) The transfer characteristic curve of an npn transistor used as a switch is shown in the figure. Vi is the base bias voltage and Vo is the collector voltage. Which portions of the characteristic curve are used for operating the transistor as a switch?

(a) AB and EF

(b) BC, CD and DE

(c) CD only

(d) AB only

(e) EF only

When a transistor is use as a switch, it operates in the saturation region EF for full conduction (switch on) and in the cut off region AB for no conduction (switch off). The correct option is (a).

[When the transistor operates in the saturation region, the base current is large so that the collector current also is large. Almost the entire collector supply voltage will then be dropped across the resistance connected to the collector lead so that the emitter to collector voltage will be very small. The transistor will operate in the cut off region when the emitter to base voltage is insufficient to forward bias the emitter base junction and to make the transistor conduct. Consequently there is no voltage drop across the resistance connected to the collector lead so that the entire collector supply voltage appears on the collector].

You can access all posts on electronics on this site by clicking on the label, ‘electronics’ below this post.

Tuesday, December 03, 2013

Apply Online for AIPMT 2014



Now is the right time for you to apply online for the All India Pre-Medical/Pre-Dental Entrance Test (AIPMT) 2014. Instead of the National Eligibility Cum Entrance Test (NEET) conducted last year for admitting students to MBBS and BDS courses, the earlier AIPMT has been reintroduced. The Entrance Test which will be conducted from 10 am to 1 pm on 4th May, 2014 (Sunday) will have one paper with 180 objective type questions from Physics, Chemistry and Biology (Botany & Zoology).
The last date for submission of online application without late fee is 31-12-2013.
The last date for submission of online application with late fee is 31-1-2014.
Visit the AIPMT site at http://aipmt.nic.in immediately to get all details.

Monday, October 07, 2013

Multiple Choice Questions Involving Electromagnetic Induction



“There is only one corner of the universe that you can be certain of improving, and that’s your own self.”
– Aldous Huxley


Many questions on electromagnetic induction have been discussed on this site earlier. You can access those questions by clicking on the label, ‘electromagnetic induction’ below this post. Today we shall discuss a few more questions in this section.

(1) An object of mass M (Fig.) carrying a charge +Q is released from rest at the top of a smooth inclined plane of inclination ฮธ. A magnetic field of flux density B acts  throughout the region and is directed normally into the plane of the figure. Which one among the following statements is correct?
(a) The acceleration of the object down the incline depends on Q but does not depend on B.
(b) The acceleration of  the object down the incline depends on B but does not depend on Q.
(c) The acceleration of the object down the incline depends on both Q and B.
(d) The acceleration of the object down the incline does not depend on Q and B.
(e) All the above statements are incorrect.
The component of the gravitational force along the incline is Mgsinฮธ which can produce in the object an acceleration gsinฮธ down the incline. When the object moves down along the inclined plane, the magnetic force (Lorentz force) acting on the object is directed perpendicular to the inclined plane such that it tries to press the object against the inclined plane.
[Apply Fleming’s left hand rule to arrive at the direction of the magnetic Lorentz force].
Since the magnetic force on the object is perpendicular to the inclined plane, it has no component along the plane. The acceleration of the object down the incline is gsinฮธ itself and is independent of Q and B [Option (d)].
(2) In the above question suppose the inclined plane is rough and the object is able to slide down. Which one among the following statements is correct?
(a) The acceleration of the object down the incline depends on Q but does not depend on B.
(b) The acceleration of the object down the incline depends on B but does not depend on Q.
(c) The acceleration of the object down the incline depends on both Q and B.
(d) The acceleration of the object down the incline does not depend on Q and B.
(e) All the above statements are incorrect.
In this case the frictional force acting between the object and the inclined plane reduces the acceleration of the object. The frictional force F depends on the normal force N acting on the object.
[Remember that F = ฮผN where ฮผ is the coefficient of friction]
But the normal force (which is Mgcosฮธ + magnetic Lorentz force) depends on both Q and B since the magnetic Lorentz force is QvB where v is the velocity of the object.
Therefore, the acceleration of the object down the incline depends on both Q and B [Option (c)].

(3) A plane rectangular coil of length 2L and breadth L has N turns of insulated copper wire in it. Initially (at time t = 0) the plane of the coil is perpendicular to a uniform magnetic field of flux density B . The coil rotates with angular velocity ฯ‰ such that the axis of rotation of the coil is at right angles to the magnetic field (Fig.). If the voltage induced in the coil is Vmaxsinฯ‰t, the angular velocity of the coil is

(a) Vmax / 2NL2B

(b) 2Vmax t / NL2B

(c)Vmax/NL2B                                                                                            

(d) NL2B/ Vmax

(e) 2NL2B/ Vmax

The magnetic flux ฯ† linked with the coil at the instant t is given by      
ฯ† = NAB cos ฯ‰t where A is the area of the coil.

The voltage V induced in the coil is is given by

            V = – dฯ† /dt = NABฯ‰ sin ฯ‰t

It is given in the question that V = Vmaxsinฯ‰t

Therefore, Vmax = NABฯ‰

This gives ฯ‰ = Vmax /NAB
Since the area A = 2L2, we have ฯ‰ = Vmax / 2NL2B


(4) In the transformer shown in the adjoining figure, the secondary winding has taps A, B, C, D and E. The number of turns between taps A and B is 100. The number of turns between taps B and C is 50, the number of turns between C and D is 40 and that between D and E is 10. The primary has 2000 turns and is connected to 220 volt A. C. mains. Between which taps will you obtain 5.5 volt output? 

(a) Between A and B

(b) Between A and B as well as B and E

(c) Between B and C as well as C and E

(d) Between C and D

(e) Between D and E

Since the primary voltage is 220 V and the number of turns in the primary is 2000, the induced voltage per turn is 220/2000 = 0.11 volt.

Therefore, the number of turns required to produce a voltage of 5.5 volt is (5.5)/(0.11) = 50.

Since there are 50 turns between taps B and C as well as between taps C and E, the correct option is (c).

[You can work this out this way also:

Considering the entire secondary of the transformer, the secondary to primary turns ratio is 200/2000 = 1/10. Therefore, the secondary voltage (between the ends A and E) is 220/10 = 22 V. Since the voltage across the entire secondary containing 200 turns is 22 volt, we will get 5.5 volt across 50 turns (between taps B and C as well as between taps C and E)]
 

Thursday, August 22, 2013

JEE (Advanced) 2013 Questions Involving Two Dimensional Motion



"It is unwise to be too sure of one's own wisdom. It is healthy to be reminded that the strongest  might weaken and the wisest might err”
– Mahatma Gandhi


Today we shall discuss three questions which appeared in JEE (Advanced) 2013 question paper. JEE (Advanced) is the examination conducted for admitting students to under graduate engineering programmes in IITs, IT-BHU and ISM Dhanbad (in place of the earlier IIT-JEE).

(1) A particle of mass m is projected from the ground with an initial speed u0 at an angle ฮฑ with the horizontal. At the highest point of its trajectory, it makes a completely inelastic collision with another identical particle, which was thrown vertically upwards from the ground with the same initial speed u0. The angle that the composite system makes with the horizontal immediately after the collision is

(a) ฯ€/4

(b) ฯ€/4 + ฮฑ

(c) ฯ€/4 – ฮฑ

(d) ฯ€/2

At the highest point (P in fig.) of the trajectory, the velocity of the first particle is u0 cos ฮฑ.
[The vertical component of the velocity of projection of the first particle is zero at P. The horizontal component (u0 cos ฮฑ) of the velocity of projection is retained through out the trajectory]
The momentum of the first particle at the highest point P is mu0 cos ฮฑ and is directed horizontally rightwards.
The velocity (v) of the second particle at the point P is given by the equation of linear motion, v2 = u02 – 2gH. This gives
            v = √(u02 – 2gH)
But H = (u02 sin2ฮฑ)/2g
Therefore we have
            v = √[u02 – 2g(u02 sin2ฮฑ)/2g] = √[u02(1 – sin2ฮฑ) = u0 cos ฮฑ
Therefore, the momentum of the second particle at the point P is mu0 cos ฮฑ and is directed vertically upwards.
The momentum of the composite particle immediately after the inelastic collision is the resultant of the momenta of the two particles. The resultant of the horizontally rightward momentum mu0 cos ฮฑ and the vertically upward momentum mu0 cos ฮฑ is inclined at 45ยบ with respect to the horizontal.
Therefore, the correct option is (d).
*          *          *          *          *          *          *          *          *          *          *          *         
Two more questions are discussed below. These questions too are single correct answer type multiple choice questions and are based on a given paragraph.
Here is the paragraph and the two questions related to it:

A small block of mass 1 kg is released from rest at the top of a rough track. The track is a circular arc of radius 40 m. The block slides along the track without toppling and a frictional force acts on it in the direction opposite to the instantaneous velocity. The work done in overcoming friction up to the point Q, as shown in the figure below, is 150 J. (Take the acceleration due to gravity, g = 10 ms–2)   
(i) The speed of the block when it reaches the point Q is
(a) 5 ms–1
(b) 10 ms–1
(c) 10√3 ms–1
(d) 20 ms–1
The block reaches the point Q after falling through a height h equal to R sin30ยบ = R/2. Therefore it loses gravitational potential energy mgh. Out of this energy 150 joule is used up against friction and the remaining portion is transferred to the block as kinetic energy ½ mv2 where v is the speed of the block at the point Q. Therefore, we have
            mgh – 150 = ½ mv2
Here m = 1 kg, g = 10 ms–2 and h = R/2 = 40/2 = 20 m
Therefore, 10×20 – 150 = v2/2
This gives v = 10 ms–1
(ii) The magnitude of the normal reaction that acts on the block at the point Q is
(a) 7.5 N
(b) 8.6 N
(c) 11.5 N
(d) 22.5 N
 
 
With reference to the adjoining figure, if the normal reaction acting on the block at the point Q is N, we have

            N – mg cos 60 = mv2/R

[mv2/R is the centripetal force required for the circular motion of the block]
Therefore N = mv2/R + mg cos 60 = (1×102)/40 + 1×10× ½  = 7.5 newton.