1. Can we calculate the resistor if it is installed in circuit board?

You can measure a resistor in a circuit but the circuit will most likely affect the value read (usually making it look lower in resistance). A simple example would be if there were two resistors in parallel in the circuit. If you measure one, you will get the resistance of the two in parallel, and maybe other effects of the rest of the circuit.

Most resistors have markings on them, and they rarely fail unless they are cooked by too much power. That is the easy way. If they are not marked, you want to know the value, and it is in a circuit, then it is hard to figure out the value. It might be easier to unsolder one end of it and then measure it.

2. How is the transmission of a signal in a computer over x number of clock cycles translated into binary?

All computer logic today uses FETs as switches. A FET is a switch with gain, meaning that a small signal change on its input (the Gate) causes a bigger signal in the Drain. Bigger does not mean bigger voltage, it usually means more current at the same voltage, so it can drive many other inputs after it. Two FETs can be connected together to make a logic gate, like an AND function. In addition, gates can be connected together to make flip-flops and counters and adders, etc.

Logic "1" is usually a higher voltage than logic "0", and logic 0 is usually zero volts. In newer processors, the high voltage is less than a volt, since the FETs are so small that 1.5V will blow them up.

Therefore, it is not the presence of a signal or the lack of one; it is a high voltage and a low voltage. There is nothing that the computer translates, that voltage is it, throughout the computer. That is what binary means, one of two voltages. There is no clock involved to make something binary all signals in the computer are all binary logic with a voltage. Even a clock is just a logic signal that goes between 1 and 0 at a periodic rate.

3. How can the electromagnetic can travel in air and not lose any information contained in them?

There is a limit to how far you can get television signals. The power is spreading out the farther you are away from the source. At some distance, you reach a point where the noise in the atmosphere becomes greater than the signal, and you can no longer extract all the information from the signal. Digital television has much error correction, many bits are sent just so corrections can be made when there are errors. This helps on the fringe, but even this fails when the signal gets weak enough. However, error correction makes the signal perfect until you hit that exact point where the correction fails. Thus, digital TV has a sharp cutoff point - you get a perfect picture, or it goes away completely. Therefore, electromagnetic waves do lose information. Think of someone aiming a flashlight at you. The person walks further and further away from you. At some point, you are just not going to be able to tell. What if there were fogs or lots of pollution in the air? Alternatively, 20 other flashlights and you had to pick out just the one. It is easy and 100% when they are close.

4. Can you explain electricity at atom level and if possible show some diagrams please

If you look at the classic Bohr model of the atom (from 1913), you have electrons orbiting around a nucleus of protons and neutrons. Normally there are as many electrons (negative charge) as protons (positive charge), so the net charge of the atom is zero. The various shells or orbit radii of the model have different characteristics as to how many electrons they are happy having orbiting in them. The first shell likes 2 max, the 2, and 6, etc. If there is one less electron that what the outermost used shell considers full, it will happily take on another electron, even if this unbalances the charge. If it has just one electron in a shell, it would happily give it up even if it unbalances the charge. Copper, one of the best conductors of electricity, has 29 electrons, which means in its 4th orbit, it has one electron. It is easily taken away by something pulling on it. In fact, if you put a bunch of copper atoms together, there is a cloud of electron sharing with that one electron moving from atom to atom, and others taking its place.

5. What is the difference between Photodiode and Solar cell?

A photodiode is made to detect light quickly a solar cell is made to collect energy from light. They are both typically silicon diodes, but modified to meet their different requirements. A photodiode has to be fast, which means low capacitance, which means small area of silicon. Therefore, it is not very sensitive, and cannot generate much power from light. A solar cell has as large an area as you can afford to buy, getting watts per square inch. There are other differences in the way they are made, and how the PN junction is grown, but they all relate to this difference in purpose.

6. The current through a resistor of 50 ohms in an AC circuit at t = 0.008 s is 65% of the peak value. The smallest possible frequency of the generator delivering the current is

If it is then this is easy, you take the arcsine of 65% that gives you what angle you are at in the sine cycle, take the ratio of that to 360, and multiply that by 8mS to get the time of a full cycle, and then take one over that to get frequency. This will be the lowest frequency. Note that the 50 ohms has nothing to do with it, other than implying it is an RF circuit where 50 ohms is common. You say "smallest possible frequency" which also is not very clear I will assume you mean lowest frequency. There is no highest frequency you can meet this requirement with an arbitrarily high frequency.

7. What is the significance of "4-20 mA" signal in hart protocol?

The HART protocol is an old Frequency Shift Keying way of sending data, typically from highway sensors. This is a very old standard by today's standards there are so much better ways to send data. Of course, 4-20 ma loops are even older, dating back over 50 years, and still in common use. Must be something good about it - it is simple.

4-20 ma loops are a way to send an analog value, like temperature or position, over a pair of wires. It is simple on the surface, 4 mA is the minimum, and 20 mA is the maximum of the range. The cool thing about this is that it is constant current, not a voltage, so line resistance does not matter. Anything, constant current looks like an open circuit, so it is supposedly immune to noise (though in reality it still has noise pickup problems). However, why not 0 to 20 mA the cool thing is you can power the remote sensor. You are running a current through the remote you have a voltage at the driving end why not use some of that power to run the electronics in the sensor? Therefore, if the sensor pulls less than 4 ma and you make the range 4-20, you always have enough current to power the remote at the same time.

8. Is it possible to build an AC or DC variable-speed generator with a variable field current, controlled by a signal from a torque sensor connected to the shaft of the generator (i.e., net torque = 0)?

You can control the field with anything, but why would you do it with torque? Why do you say net torque=0? What is the significance of variable speed?

I am trying to think of why you would do this. If the torque were low, you could increase the field to generate more energy, which would make the torque go up. That is positive feedback, but maybe it is constant power into a resistive load (voltage would go up). If you did negative feedback, that would mean the field would reduce as the torque went up, reducing the torque, so you would have a torque regulator. This would probably be good for a wind generator, as you want to control the torque to match the wind speed to get maximum energy out, but this would also vary the output of the generator a lot. Maybe if you were heating water this would work.

9. Do you have any ideas how to make a ping-pong ball launcher that reloads automatic and shoots automatically?

Air cannon is probably the simplest, PVC pipe from Home Depot and shoots things very far, can make any size you want, need a tire pump or air compressor to power it. It is also called Potato Cannons for obvious reasons. I shot a potato over 1000 feet with 60 psi and 2" pipe.

10. What are encoder and the decoder? What are the uses of these two devices? Also, write about how it works with circuit diagram.

There are zillions of things in electronics called encoders. You can look up LCDs and NAND gates as well and this is really basics.