Suppose there are a few resistors in series in a circuit with which an emf source (like a battery) is connected. Now how to find the voltage drops in each resistor? One way is to find the current first by using the formula I = E/(Req +r). Here Req stands for equivalent resistant of the external circuit and r is the internal resistance of the battery. After evaluating the current you can now use Ohm’s law (V = IR) to find the individual voltage drop across each resistor including the internal resistance.
Another way is using Voltage divider rule. Suppose there are two external resistors R1 and R2 and the internal resistance is r. So using the voltage divider rule the voltage drop across R1 is E*R1/(R1+R2+r). The same way voltage drops across R 2 and r can be found as well.
Current divider rule
Now about the current divider rule. In this case, the resistors have to be connected in parallel. Suppose two resistors (and probably this rule works only for two resistors only, not for three resistors) are connected in parallel. And the magnitude of the total current flowing through them is I. then by using current divider rule, the current through R1 is I1 = R2 * I /(R1 + R2) and that through R2 is I2 = R1 * I / (R1 + R2). This law/rule indicates that current in any parallelly connected resistor is inversely proportional to its resistance, which is evident from Ohm’s law. This is because, the voltage drop across the parallel combination is constant in this case.
I bought this land one year ago. I have made here some establishments (a house) and then I built a fence around my garden. Well, while putting the fence the person representing the previous owner (of the land) helped me in doing that and during this time he made me put a few of the pillars more inside than I expected. The thing is there was no demarkation pillar previously, it got lost in some mysterious way.
So I got suspicious and wondered whether the person I mentioned above was depriving me of my rightful share of land in some tactical way. That’s when I decided to measure my land. I took measures of the four sides and the map of the land looks like following (all the numbers are in feet):
There should be 5 decimals (shotangsho) of land in it. For your information, 1 decimal or shotangsho I’m referring here is equal to almost 434 sq. feet. So 5 shotangsho land should be 5*434 = 2170 sq. feet approximately in size. Let’s measure it now, with all the knowledge that I have acquired from geometry and algebra. Here it is given that the angle between 70 and 29 feet sides is a right angle, but the one between 31 and 70 feet sides might not be. We redraw the picture and mark it like the way given below:
Triangle ABC being a right triangle, the angle ABC is 90 degrees; hence the length of the hypotenuse AC should be the sq. root of (sq. of AB + sq. of BC) = the sq. root of (sq. of 70 + sq. of 29) = the sq. root of (4900 + 841) = the sq. root of 5741 = 75.8 feet (almost)
So the half-perimeter (s) of triangle ACD is = (AC+CD+AD)/2 = (75.8+76+31)/2= 91.4
Hence the area of the traingle ACD is = sq. root of s*(s-a)*(s-b)*(s-c) = sq. root of 91.4*(91.4-75.8)*(91.4-76)*(91.4-31) = 1151.6 sq. feet
And the triangle ABC being a right triangle, its area is = 0.5*height*base = 0.5* 70*29 = 1015 sq. feet
So the total area of my land is approximately = (1151.6 + 1015) = 2166.6 sq feet which is very close to 2170 sq. feet. Hence it may be concluded that there was no manipulation from the aforementioned representative while putting up the fence along the perimeter of my land.
Something that is considered a work in daily life may not be considered a work when it comes to physics. Take the job of a watchman for example. Even if he barely moves, he is said to have completed his task at the end of the day in daily life terms. But it’s not the same in the language of Physics. Some will opine that an object has to move to do some work according to physics. Well, it is not 100% correct either. (This article is on the topics Work, positive work and negative work.)
Actually, in order to do some work in Physics, you have to fulfill three conditions:
(1) You have to apply a force on a body
(2) It will have to move
(3) But the direction of movement must not make 90 degrees angle with that of the force applied.
That’s why work (usually denoted by the letter W) is expressed as: W=FScosθ
So work done is the product of the magnitude of force, that of the displacement and the cosine of the angle between the force and the displacement. If any of the above-mentioned three quantities becomes zero, the work done becomes zero as well.
Consider these three cases of work done being zero
First of all consider a case where F=0, S≠0. In the space, far far away from the earth and all other planets and stars, there might be place where the gravitational field is absolutely zero. In a place like that, if an asteroid or any other object is moving with a constant speed (constant speed is expected since no force is acting on the object), then no work is done on the object although displacement is not zero (S≠0). Because in this case no force is acting on the object (F=0). (This article is on the topics Work, positive work and negative work.)
Second of all we will consider a case where F≠0, S=0. Suppose that you’re pushing/pulling an object with no avail, i.e. you failed to move it. So the displacement is zero in this case although the applied force is not. That’s why the product FScosθ will have a zero value as a whole. Thirdly we are going to consider a case where neither the force nor the displacement is zero, still the work done is zero. In such cases the quantity cosθ (which is the cosine of the angle between the force and the displacement) is zero.
The orbital path of the moon around the earth is fairly (or exactly) round. That’s why every moment the incremental displacement takes place in a direction perpendicular to that of the gravitational force on the moon by the earth. So θ=90 degrees and cosθ=0; hence the work done by the gravitational pull is zero. In this case the gravitational pull acts like a centrifugal force. When a body revolves around in a circular path the work done by the centripetal force is always zero. (This article is on the topics Work, positive work and negative work.)
Now that we have explained ‘Work’ enough, let’s come to know what positive work and negative work are. When the angle between the force and the displacement is less than 90 degrees, then the work is found positive, that’s why such work is called positive work. This sort of work is also called ‘Work by force’. On the other hand, when the angle between the force and the displacement is greater than 90 degrees, then the work is found negative, that’s why such work is called negative work. This sort of work is also called ‘Work against force’. (This article is on the topics Work, positive work and negative work.)
Suppose you’re pulling or pushing a trolley and it is moving in the direction you intend it to, then your work done on the trolley is definitely positive. Again, you’re holding a duster and moving it upwards vertically. Positive work is done for the force you’re applying on it, but negative work is done by its weight (gravitational pull); because in that case the angle between the gravitational pull and the displacement is 180 degrees and cos180= -1. So whether positive or negative work is done depends on which force is being considered.
Centrifugal force is called a virtual force. Because when an object revolves around in a circle, it feels that someone or something is pushing it outwards from the center. Actually no one is pushing, the force is felt from somewhere
ACCOUNT SUSPENSION & RECOVERY
A daily-life example of centrifugal force
Suppose that you are sitting in a bus. At this time the bus starts to turn right/left, it starts moving in a circle. The upper portion of your body will be tilted, it will be pushed outwards from the center. This happens basically due to inertia. According to Newton’s 1st law of motion, if no force is applied on you from outside, then you’re supposed to move in a straight line. Since the lower portion of your body is rigidly connected with the bus, that’s why it starts turning when the bus does. But the upper portion of your body is fairly free, that’s why it tends to move in a straight line as before. This is the reason why your upper body tilts and seems to move away from the center of the circular path.
Suppose you took a window seat and your upper body gets in contact with that of the bus due to the tilting effect and the feeling of ‘being pushed away’. In that case the body of the bus will put force on your upper body and thus make it move in a circular path (this force is basically centripetal force which is mandatory if a body wants to revolve in a circle). Although you will feel that someone or something is pushing you to make your upper body being pressed against that of the bus.
The force you thought was centrifugal is actually centripetal
So from the above discussion it is evident that no one or nothing applies a force on you from the center of the circular path. You just feel a centripetal force which is supplied from some other source you didn’t even think of. In the above example, the centripetal force is supplied by the body of the bus. According to Newton’s 3rd law of motion, your body also applies a force on the bus. These two forces are equal in magnitude, but acting in opposite directions. Keep in mind that the two forces mentioned in Newton’s 3rd law of motion applies on two different objects, not on a single object. Had these two forces been acting on the same object, they would eventually cancel each other.
So now you know why centrifugal force is called virtual force. When you move in a circle, you seem to feel it, you feel that something is pushing you away from the center. Actually nothing of this sort is happening. A force is definitely being acted upon your body, but it is the centripetal force, NOT centrifugal.
In order to determine the equation and the graph of a straight line you just need two conditions. It could be two points, or one point and the slope, or intercepts from the axes etc.
If a straight lines passes through points (x1,y1) and (x2,y2) then the equation of the line is as follows:
If a line passes through point (x1, y1) and has the slope of value m, then its equation is:
If a straight line has intercepts of values a, b respectively from X and Y axes then its equation would be:
Now if a straight line has a distance of p from the origin and the perpendicular line-segment from the origin to it makes an angle of Q with the positive X-axis, then its equation is:
As you can see from the above analysis that two conditions are enough to determine a straight line.
Now I am going to create a philosophy of the above example. A person’s character is like a straight line, with a very few exceptions. Suppose you get introduced with a new person; you may find him a nice person, or an average one. Before you finally trust him/her with something, be sure to check him at least twice. Pretend that you assigned him something. If he repeat the same kind of mistake, then you can conclude that he is an erroneous person. If you trust someone with something and find that he breaks your trust twice, then surely he’s a person not to be trusted.
Personal experience stating the reason for bringing this up
I present this example because recently I have gone through an experience which very much resembles the straight-line case. The person who disappointed me is none other than my FIL. Back in 2011 I graduated and joined a publications company, everything was going fine for me. That’s when my FIL advised me to leave that job and promised to get me a better one. I listened to him, but he was unable to fulfill his promise (couldn’t find me a job that he promised). I was very frustrated and financially devastated for a couple of months. However I recovered myself and found myself a new job.
Recently I relied on my FIL for another matter. He has been repeatedly suggesting me to buy some land now that I have some money in my hand. I listened to him. After all I gotta ensure my wife’s and my child’s future (recently I became a father). So I asked my FIL to find me some suitable land, he did that. Although the land is pure and not at all controversial, but the owner might not be. My FIL proposed me to make some ‘advance payment’ and then at a later time pay the rest of the money. I agreed to do that and paid the advance money.
The problem is that the ‘advance deed’ was a open one and now-a-days no open (unregistered) deed is accepted at court. So at the end of three months period (as depicted in the deed) I can’t possibly legally put pressure on the owner lady to accept the rest of the money and thus register the land in my name.
The conclusion and decision
This time too I got caught because of my FIL, because he should’ve known that no open deeds are accepted at court now-a-days. Now I’m running the risk of losing my advance money which is a pretty big amount for me. Then again I can lodge a money-suit against that lady if she tries to play very tricky. The point is that I’m never going to trust and rely on my FIL again. Like a straight line I’ve got two points about him and now I am able to draw that line which would depict his character: HE’S NOT TO BE TRUSTED.
Is there really a basis for voltage, pressure and temperature relationship?
Consider two charged bodies – direction of flow of charge between them doesn’t depend on the relative amount of charges on the bodies. It depends on the potential difference between them. It is a misconception that if they are connected by a wire the body with more charge will lose charge and the other will gain charge until the amount of charge is equal on both the bodies. (This article is on voltage, pressure and temperature relationship.)
Actually the thing is that charge will flow from one body to other if the charge density on the bodies are unequal. It will keep flowing until the charge density is equal on both the bodies. Charge density is a measure of electric potential. The more is the charge density on a particular object, the more is its electric potential. The two charged bodies will transfer charge from one to another because charge constitutes of elections. They repel one another due to having same kind of charge.
A practical life example
Now consider two rooms with unequal space and the number of people in those might be equal or unequal. Just think that density of people in those two rooms are unequal. If the two rooms are connected by a passage, some people will have a tendency to migrate from one room to another. Because too many people in a single room makes it congested and inhalation of the people gets obstructed. The shift of people from one room to another will continue until the density of people becomes almost equal on both the rooms. (This article is on voltage, pressure and temperature relationship.)
The same thing is applicable for pressure. If we connect two cylindrical containers of water by a pipe at their lower end, water will definitely transfer from one to another. But the direction of flow will depend on relative height of water-column in the containers, not on the amount of water in them. If the thick container has more water in it but lower height of water column then it will lose water, the other will gain.
Role of temperature in heat science
Now about temperature. If we connect two bodies thermally, one will lose heat and the other will gain. This transfer of heat and direction of flow will not depend on relative amount of heat in the two bodies. it will depend on relative temperature, or temperature difference. The hotter body (the one with greater temperature) will lose heat even if it might be the one with less amount of heat. The other will gain heat if it has lower temperature, even if it is the one with greater amount of heat. Here comes the idea of ‘Heat capacity’. The second body will gain further heat although it already has greater amount of heat, just because its heat-capacity is greater. (This article is on voltage, pressure and temperature relationship.)
A couple of bulbs connected in series, if one of them is fused, none of them will glow anymore. And you can not say for sure which one is fused, unless you manually check each and every of them. Series connection hazardous real life. These are the hindrances and drawbacks of series connection.
Then again, there are some advantages too, like: you can switch on or off all the lights or electrical appliances in series just with a single switch. Series connection is not effective, when there is a significant voltage drop in each appliance. For example, if the bulbs used in street-lighting are such in structure that each causes a small drop in potential, then there will be gradual drop in effective potential difference for the rest of the bulbs and thus they will glow dimmer. So when planning to put a few appliances in series, you have to keep these factors in mind. Series connection hazardous real life
Now I am going to give an example of series connection-type scenario in real life. You know about youtubing. The job of uploading videos to one’s youtube channel and monetizing those and thus earning money is called youtubing. In order to do successful youtubing, you must not (i) steal someone else’s video (ii) get community strikes (iii) use misleading metadata (iv) post bad comments in someone else’s videos that can be marked as spam and many other factors. If any of these goes against the rules, Google might simple terminate your channel without showing any reason.
This is why, a Youtube user, when has his account suspended, often claims that they did nothing wrong. Actually the thing is that they just don’t realize what they did wrong. It’s like that ineffective series connection where at least one appliance is out of order and you don’t know which one it is. Series connection hazardous real life