Boolean expression for logic circuit (a)

10

400 10₃ 25 10 ⁶A 25mA and V_CC – V_CE = I_CR_C

I_C =

×10 = × ⁻ =

3 10₃ 3 33 10. ³ 3 33. mA

b = = ×

× ₋⁻ = I

I^C_B

3 33 10

25 10. ₆³ 133 18. (i) For n-type region,

n_e =N_D = 1 × ×

10₆ 5 10²⁸= 5 × 10²² m^–3

 1 1

10⁶ ppm =



 

As ⁿen_h = ⁿ_i², 

n n

h ni

= e = ×

×

−

−

2 16 3 2

22 3

1 5 10 5 10

( . m )

m = 0.45 × 10¹⁰ m^–3 For p-type region,

n_h=N_A =200× ×

10₆ 5 10²⁸= 1 × 10²⁵ m^–3 Now, n n

e ni

= h = ×

×

−

−

2 16 3 2

25 3

1 5 10 1 10

( . m )

m = 2.25 × 10⁷ m^–3 (ii) The minority carrier holes of ⁿ-region wafer (n_h = 0.45 × 10¹⁰ m^–3) would contribute more to reverse saturation current than minority carrier electrons of ^p–region wafer (ⁿ_e = 2.25 × 10⁷ m^–3) when p – n junction is reverse biased.

19. Boolean expression for logic circuit (a)

A Y = A

Here the given NOR gate with A Y

01 1

short circuit input is acting as 0 NOT gate. Its truth table is

Boolean expression for logic circuit (b)

So by De-Morgan’s theorem Y =

(

)

Hence, the logic circuit acts like AND gate.

Its truth table is

A B Y

00 11

01 01

00 01 20. According to diagram,

V_max =100 =

2 50 V , V_min= 20= 2 10 V

V

100 V 20 V

t

(i) Percentage modulation, P = m × 100

where m = modulation index = −

Comparing with the standard A.M. wave, c_m(t) = A_c(1 + m cos w_m t) sin w_c t,

(i) Minimum amplitude of A.M. wave

= A_c – mA_c = 5 – 0.6 × 5 = 2 V.

Maximum amplitude of A.M. wave

= A_c + mA_c = 5 + 0.6 × 5 = 8 V.

(ii) Frequency components of the A.M. wave are f_c – f_m, f_c, f_c + f_m i.e., 336 – 1,336,336 + 1 or 335 kHz, 336 kHz, 337 kHz.

(iii) The amplitudes of the three components are mA A A^c _c m ^c

23. (a) Initiative, curiosity, scientific awareness, community service.

(b) Light emitting diode (LED) is a junction diode made of gallium arsenide or indium phosphide in which when hole-electron pairs recombine at forward biased p-n junction, energy is released in the form of light.

The principle on which LED works is spontaneous emission of radiation, when an electron jumps from higher energy level to lower energy level in a semiconductor atom. At forward biased p-n junction, free electrons of n-type combine with holes of p-type semiconductor. As free electrons lie in conduction band and holes lie in valence band, so electron falls from the higher to lower energy level containing holes and the energy is released in the form of radiation. The energy of radiation emitted by LED is equal to or less than the forbidden energy band gap E_g of the semiconductor used, and is given by hu hc E_g

= λ = .

The frequency of emitted radiation in LED, thus depends upon the band gap energy E_g of the semiconductor used. The intensity of emitted radiation in LED depends upon the forward current flowing through the LED. More the forward current flowing through the LED, more the hole-electron pairs combine at forward biased p-n junction, releasing more number of photons and hence larger will be the intensity of emitted radiation.

24. Refer point 9.3(4,5) page no. 588 (MTG Excel in Physics).

Refer point 9.4(8) page no. 595 (MTG Excel in OR Physics).

25. Refer point 9.2, (2 (a, b)) page no. 585 and point 9.3(6(ii)) page no. 588 (MTG Excel in Physics) Refer point 9.1 (3,4,5,6) page no. 583 (MTG Excel OR in Physics)

26. Refer point 9.4 (9) page no. 595 (MTG Excel in Physics)

Refer point 9.3(6(i), 7(i)) page no. 589 (MTG Excel OR in Physics)

nn

Q1. When you load up a plastic shopping bag with groceries and then carry the bag by the loops at the top of the bag, why will the loops initially withstand the load but then, several minutes later, begin to stretch, perhaps to the point of tearing?

– Akash Jain (UP)

Ans. If you suspended a load from the lower end of a spring hanging from a ceiling, the spring will stretch by a certain amount and then stay stretched.

Plastic, which consists of polymers, is different. If you suspend a load from the lower end of a plastic strip, the strip will initially stretch like the spring but thereafter it will gradually stretch more in what is called viscoelastic creep. The mechanism of this creep can vary from polymer to polymer.

The polymer consists of many long and entangled molecules. When the polymer is put under load, these molecules gradually disentangle somewhat because very are pulled in the direction of the load. The gradual reorientation of the molecules allows the plastic to gradually stretch.

Q2. What causes the tides? Why do most shore locations have two high tides per day but others have only one?

– Sahil Verma (Delhi)

Ans. The primary cause of tides is the Moon’s gravitational pull on Earth’s oceans even though that force is not strong enough to lift the water.

Because the force varies over Earth’s surface (strongest on the side facing the Moon, weakest on the opposite side), the force reshapes the water distribution by stretching it parallel to the line connecting Earth and the Moon. The stretching Do you have a question that you just can’t get answered?

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produces two bulges in the water distribution, one on the side facing the Moon and one on the opposite side. If Earth did not rotate, then a shore location in the bulge facing the Moon would have high water (high tide) all day and a shore location in the opposite bulge would as well. However, Earth’s rotation means that a shore location rotates through both bulges in about a day and will thus have two high-water intervals.

The bulges are not exactly positional on a line through Earth and the Moon because the water motion encounters friction within the water and against shorelines. The friction delays the water’s response to the stretching by the Moon. So, the high-water point in a port city may occur an hour or more after the Moon is highest in the sky.

Another complicating factor is that the gravitational force from the Sun also tends to stretch the water distribution. However, the solar effect is, roughly less than half the lunar effect. Although the Sun is much larger than the Moon, it is also much farther from Earth. During New Moon and Full Moon, the Sun and Moon are aligned and their tidal effects sum to give larger tides called spring tides. When the directions to the Sun and Moon are separated by 90°, the sum gives neap tides. Because of these various complications some shore locations can have only one noticeable tide per day.

Q3. When an airplane flies somewhat overhead and close enough to be heard, lower your head by stooping to the ground. Why does the frequency of the airplane noise increases as you lower your head ?

– Shreyas (Haryana)

Ans. The sound you hear consists of the sound coming directly to you from the airplane and the sound that reflects to you from the ground. The two sets of sound waves undergo interference at your ears and you hear primarily the waves that constructively interfere, they reinforce one another rather than cancel one another. The height above the ground at which constructive interference occurs depends on the wavelength, greater wavelength requires greater height. As you lower your head, you move down to the heights at which shorter wavelengths or higher frequencies, undergoes constructive interference. So, as you stoop, the sound you hear increases in frequency.



ISRO will launch India’s