Physics Test - 6

Electromagnetic waves are produced by electrically charged particle oscillates (accelerating charges). The electric field associated with the accelerating charge vibrates which generates the vibrating magnetic field. The electric and magnetic fields in most electromagnetic waves are perpendicular to the direction in which the wave moves, it is ordinarily a transverse wave.

Disadvantage of PCM is its high bandwidth. 

PCM:

• PCM stands for Pulse Code Modulation.
• With PCM, the amplitude of the analog signal is sampled at regular intervals and translated into a binary number.
• The difference between the original signal and the translated digital signal is called the quantizing error.

Some Advantages associated with PCM are:

• Immunity to transmission noise and interference.
• It is possible to regenerate the coded signal along the transmission path.
• The Quantization Noise depends on the number of quantization levels and not on the number of samples produced per second.
• The storage of Coded signals is easy.

The disadvantages of PCM includes:

• Requires larger Bandwidth.
• Need synchronization
• Not compatible with analog systems.

Huygen’s principle states that every point on the wavefront may be considered as a source of secondary spherical wavelets that spread out in the forward direction at the speed of light.

• The new wavefront is the tangential surface of all these secondary wavelets.
• Secondary sources start making their own wavelets, these waves are similar to that of the primary source
• Huygens's principle states that each point on a wavefront is a source of wavelets, which spread forward with the same speed.

The electric field of a plane electromagnetic wave is given by

\(\vec{E}=E_{0}(\hat{x}+\hat{y}) \sin (k z-\omega t)\)

Direction of propagation \(=+\hat{k}\)

\(\hat{E}=\frac{\hat{i}+\hat{j}}{\sqrt{2}}\)

\(\hat{k}=\hat{E} \times \hat{B}\)

\(\hat{k}=\left(\frac{\hat{i}+\hat{j}}{\sqrt{2}}\right) \times \hat{B}\)

\(\Rightarrow \hat{B}=\frac{-\hat{i}+\hat{j}}{\sqrt{2}}\)

\(\hat{B}=\frac{E_{0}}{c}(-\hat{x}+\hat{y}) \sin (k z-\omega t)\)

Trivalent impurities are used for making p-type semiconductors. So, Silicon wafer heavily doped with boron is a p⁺ substrate.

The potential energy at a distance \(r\) is given as:

\(\mathrm{U}=\frac{-\mathrm{k}}{\mathrm{r}}\)

In circular motion, centripetal force is responsible for the motion of an object.

\(\frac{\mathrm{mv}^{2}}{\mathrm{r}}=\frac{\mathrm{k}}{\mathrm{r}^{2}} \)

\(\Rightarrow \mathrm{mv}^{2}=\frac{\mathrm{k}}{\mathrm{r}}\)

Kinetic energy \(=\frac{\mathrm{mv}^{2}}{2}=\frac{\mathrm{k}}{2 \mathrm{r}}\)

Total energy \(=\mathrm{U}+\mathrm{K}=\frac{-\mathrm{k}}{\mathrm{r}}+\frac{\mathrm{k}}{2 \mathrm{r}}=\frac{-\mathrm{k}}{2 \mathrm{r}}\)

The material which is not a good conductor or a good insulator is called a semiconductor.

For example Silicon, Germanium, etc

• Intrinsic semiconductors: Intrinsic semiconductors have equal numbers of electrons and holes. Intrinsic means pure, and without any impurity.
• Extrinsic semiconductors: When small amount of impurity is doped in intrinsic semiconductor it is become extrinsic semiconductors.
• A superconductor is an element or metallic alloy which, when cooled below a critical temperature of the substance, then it loses all electrical resistance.

Given,

Thickness of the dielectric slab, \(t=1 cm =10^{-2} m\)

Dielectric constant, \(\varepsilon_{r}=K=5\)

Area of the plates of the capacitor, \(A=0.01 m ^{2}=10^{-2} m ^{2}\)

Distance between parallel plates of the capacitor, \(d=2 cm =2 \times 10^{-2} m\)

We know that:

Capacity with air in between the plates,

\(C_{0}=\frac{\epsilon_{0} A}{d}\)

where, \(\epsilon_{0}=8.854 \times 10^{-12}\)

\(=\frac{8.85 \times 10^{-12} \times 10^{-2}}{2 \times 10^{-2}}\)

\(C_{0}=4.425 \times 10^{-12}\) Farad

Capacity with dielectric slab in between the plates,

\(C=\frac{\epsilon_{0} A}{d-t\left(1-\frac{1}{K}\right)}\)

\(=\frac{8.85 \times 10^{-12} \times 10^{-2}}{\left(2 \times 10^{-2}\right)-10^{-2}\left(1-\frac{1}{5}\right)}\)

\(C=7.375 \times 10^{-12}\) Farad

Increase in capacity on introduction of dielectric:

\(C-C_{0}=\left(7.375 \times 10^{-12}\right)-\left(4.425 \times 10^{-12}\right)\)

\(=2.95 \times 10^{-12}\) Farad

Given,

Capacitance \((\mathrm{C})=18 \mu \mathrm{F}\)

\(=18 \times 10^{-6} \mathrm{~F}\)

Inductance \((\mathrm{L})=8 \mathrm{H}\)

Now,

Resonance frequency \((f)=\frac{1}{2 \pi \sqrt{L C}}\)

\(=\frac{1}{2 \pi \sqrt{8 \times 18 \times 10^{-6}}}\)

\(=\frac{1}{2 \pi \sqrt{144} \times 10^{-3}}\)

\(=\frac{1000}{24 \pi}\)

\(=\frac{125}{3 \pi}\)

This resonance frequency \((f)=\frac{125}{3 \pi} \mathrm{Hz}\).

Amplification of a signal is necessary in a communication systemto compensate for the attenuation.

Amplification: It is the process of increasing the amplitude and strength of an electrical signal with the help of an amplifier usually a transistor amplifier. Amplification is important to compensate for the loss of strength during its transmission across the channel. It is done at the point in the channel where the strength of the signal becomes weakened.

Attenuation: It is the loss of strength of a signal during its transmission across the communication channel.

During transmission of signals, the strength of the signal becomes weak and in that case, amplification is required to compensate for this loss of strength or attenuation.