Showing posts with label Voltage. Show all posts
Showing posts with label Voltage. Show all posts

Electrostatics Complete Lesson

Electrostatics is a branch of physics that deals with charges in the state of rest and its applications. Here in this chapter we are going to deal about charge, electric field, electric force between charges,electric intensity,electric potential,potential difference, electric potential energy,capacitor, capacity, effect of dielectric on the capacity and energy stored in capacitor etc. Detailed lessons are made about each of the topic and they are listed here below for the reference.

Electric Charge and Electric Force


Resultant Force and Coloumb's Law of Electric Force Problems and Solutions

Here are the further list of topics with complete lessons in this website.

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Potentiometer Comparison of EMF's and Determination of Internal Resistance

Potentiometer is a device used to compare the Emf’s of two cells and also used to find the internal resistance of a given cell.It works on a principle that the potential drop across a wire is directly proportional to the length of the wire through which the current is passing.




The device consists of two parts called primary and secondary circuit. The primary circuit consists of a strong battery to supply the potential requirement of the circuit. The connection from the cell is given to a long wire. This long wire is divided into pieces of wires each of one meter length and they are connected with small copper pieces of negligible length. They behaves like multiple wires connected in series and the total length is available between the copper strips.A galvanometer is connected from the wire with a connecting wire.

Comparison of EMF's of two cells

The secondary circuit consists of cells whose electromotive forces has to be compared. There is key that acts like a on and off switch and it can be used to control the flow of current through a particular cell.


In two different cases the two cells are connected in the secondary circuit separately and corresponding balancing lengths are measured with it. When the emf of secondary circuit is balanced with that of primary, the galvanometer shows zero deflection. This happens at a particular length of the wire and that length is called balancing length. We will find the balancing length with the second cell whose EMF has to be compared.

As per the principle, the ratio of EMF’s is nothing but the ratio of the balancing lengths in the two cases. Thus we are able to compare the EMF’s of two cells using the Potentiometer.

Determination of internal resistance of a cell

We need to connect cell alone first whose internal resistance has to be measured. We can find the balancing length in the circuit. In the next case, the same cell is connected to a external resistance in parallel and again balancing length is measured using the potentiometer. There we will get one more balancing length. The ratio of emf of that cell and its potential drop across a resistor is nothing but the ratio of balancing lengths.

Basing on the definition of potential drop, we can get one more relation between emf and voltage and by comparing both of them, we can measure the internal resistance of a cell as shown below.




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Kirchhoff's Law Problems and Solutions

Problem and Solution

In the given problem, two resistors are connected in parallel and current passing through the system is given to us. We need to measure the flow of current in a particular resistor.

We know that in parallel combination or resistors, the voltage flow is same and current across them is shared. It is shared in such a way that, the current in a element is inversely proportional to resistance. Basing on that concept, we can solve the problem as shown below.



Problem and solution

This problem is based on Kirchhoff’s first law. As per this law, the sum of the currents coming towards a junction is the sum of the currents leaving a junction. Basing on that we can measure the current in any branch as shown below.


Problem and solution

This problem is quite basic in nature and deals with the definition of current itself. We need to know the current in a system and we know that the current is defined as the rate of flow of charge or charge by time. We also know that the reciprocal of time is called frequency. Thus we need to find that to solve the problem.

Linear velocity of electron in a orbit is given and basing on it we can measure its angular velocity. We also know that the angular velocity can be expressed interms of frequency Thus we will be able to measure the current as shown below.


Problem

The problem is based on the connected elements in a circuit. In the given problem three resistors are connected and we know the applied voltage at each end. We would like to measure the potential at the junction. The problem is as shown below.



Solution

To solve this problem we can use basic concept of Kirchhoff first law. It tells you that the currents coming towards a point is the currents leaving the junction. We can further write current across any element as the ratio of potential difference across it and its resistance.

It is basic understanding that the voltage at the junction is more the starting point of the circuit and less than the other junctions. It is simply because current is passing from left to right in the circuit and current always flows from higher potential to lower potential.

The solution is as shown below.


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Kirchhoff's Laws and Explanation

Kirchhoff’s First Law

Current is defined as the rate of flow of charge. To know the flow of current under given voltage and resistance, we can use Ohm’s law. But when circuit becomes little complicated, it is difficult to find the current at a given junction and point. To simplify that we need to use Kirchhoff rules. There are two laws. One regarding charge conservation and other regarding the conservation of voltage.

According to Kirchhoff’s first law, the sum of the charges coming towards a junction is equal to the sum of the currents leaving the junction. This is nothing but conservation of charge that charge is neither created nor destroyed and it just flows from one place to other.

Currents coming towards the junction shall be treated as positive and currents leaving the junction shall be treated as negative. It is conventional consideration to understand the first law.

It is also called as Kirchhoff’s current law.



Kirchhoff’s second law

This law is called Kirchhoff’s voltage law. This is about conservation of voltage in the closed loop or circuit. According to this rule, the voltage available in the circuit through a cell in the form off EMF is distributed over all the elements in the circuit. Thus the sum of potential drop across all the electrical elements is equal to the EMF in the circuit.

To apply the second law, we shall follow certain convention. First this can be applied only to a closed loop or closed circuit but not to any open circuit. The completion of charge flow can happen only with the closed circuit but not in any open circuit.

We also shall choose either clock wise or anti clock wise direction in any closed loop. 

If there are multiple loops in a given problem, we shall not change this direction from loop to other and we shall use the same though out the problem.

In the path that we have chosen, if we get first negative plate of the battery and then positive plate of the battery, then we shall consider the EMF as positive and vice versa.
If the current in any electric element is along the same direction that we have chosen, we shall treat the potential drop across the element shall be treated as negative and vice versa.


In a following circuit, we have drawn a electric circuit and applied the law as shown in the diagram below.


Problem and Solution

This problem is based on Kirchhoff voltage law. As per this law the sum of EMF’s in a closed circuit is the sum of potential drops across different elements in the closed circuit. We need to find the current across a given element.

It can be easily solved by taking all the proper sign conventions into consideration as shown below.



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EMF and Internal Resistance of a Cell

Charge or current flows between two points only when there is a potential difference between the given two points. The simplest way of generating this potential difference is to provide a battery. This battery generates the required potential difference between given two points. Using some chemical process, and two plates it can do it. The driving potential difference between two plates of the battery is called as electro motive force. It is not a force, rather it is a potential difference between two plates of the battery.

The simple difference between potential difference and EMF is, we can find the potential difference between two points only when they are connected in a circuit with a battery. But EMF will be there in between the two plates even when they are not connected in a circuit. Simply EMF can exists in a open circuit where as potential difference can be found only in a closed circuit.

EMF drives the charges in the circuit. During this process of passing current in a circuit, there is some opposition to the flow inside the cell and it is called internal resistance. The internal resistance acts like a series resistance in the circuit and there will be some potential drop across it. It means all EMF given by the cell is not available in the circuit rather only the remaining part after the drop across the internal resistance. Thus the portion of the voltage available in the circuit after the drop across the internal resistance is called terminal voltage or terminal potential difference.

We can express the terminal voltage and internal resistance in terms of EMF and terminal voltage as shown in the page below.



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Resistance and Specific Resistance

Current flows from one charged particle to other when they have some potential difference between them. Basing on this a law called Ohm's law is defined. As per the law the potential difference between the two points is directly proportional to the flow of current between that two points. The proportionality is eliminated with a constant called resistance. It is a physical quantity that measures the opposition to the flow of current. It depends on the nature of the material and its physical dimensions like length and area of cross section of the materiel.

The potential difference is generated between two points using a battery with certain EMF also known as electromotive force. It is not actually force and it is a potential difference between two plates of a cell generated with a certain mechanism which leads to flow of current.

Current is defined as rate of flow of charge. It means it is charge that flows between two points per unit time. It is measured with a unit coulomb per second and is called as ampere. We also know that the charge is quantised. It means it is available as integral multiples of charge of electron. Hence we can find out the number of electrons flow between two points when one ampere current is passing through them as shown in the diagram below.


Resistance can be defined as the potential difference between two points when a current one one ampere is passing between them. Any way resistance does not depends on than rather it is directly proportional to the area of cross section of the conductor and is inversely proportional to the length of the wire.

The materials which has less resistance are capable of passing current through them and they are called conductors. All most all metals comes under this category.

Resistance varies for the same material when it is having different physical dimensions and hence it becomes not usable as a standard way of understanding the opposition to the flow of the current. Thus a proportionality is called as specific resistance or resistivity.

We can define resistivity as the resistance of a wire of unit area of cross section and unit length. It depends on the nature of the material and not on physical dimensions.


Specific resistance can be measured with  SI unit called ohm-meter and it is defined as shown below.


Variation of resistance with temperature

Resistance of any material varies with temperature. How does it varies depends on the nature of the material. Some materials resistance increases with temperature and for some other material, it decreases with temperature.

To measure this variation, we need to use a constant called temperature coefficient of resistance. The change in the resistance is directly proportional to its initial resistance and also directly proportional to the rise in temperature. The proportionality is eliminated with a constant and is called coefficient of resistance.


Variation of resistance with length

In general resistance of a wire is inversely proportional to its length when other parameter, area is constant. But if no information is given regarding area in any case, we shall convert that area also in terms of length. We can use the concept that volume of a body remains constant and it is the product of area and length.

Thus it can be proved that resistance is inversely proportional to the square of the length as shown in the written notes below.


Similarly, we can write the variation of resistance only in terms of area,radius and mass of the wire as shown in the below page.


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Energy Stored in Capacitor and Effect of Dielectric on it

Capacitor is a device used to store electric energy in it using the two plates. In storing the charge between the plates, we shall do some work and all that work done is stored in the form of energy between the plates.

To store small amount of charge, we shall do some small amount of work and it can be measured using the definition of potential. Any way that gives only small amount of work done. We need to store lot of small charges together in between the plates to get the total large charge. For doing that, we shall do large amount of work done. It is nothing but the sum of all small works done together. This can be obtained by integrating the basic equation as shown below.


Thus as shown in the above case, we can express the energy stored in a capacitor in the form of charge and potential. We can also express it in the form of capacity and voltage as  shown in the above diagram.

Effect of dielectric materiel on the energy stored of a capacitor

The effect of dielectric has to be studied in two possible different cases. The first case is when the dielectric is placed and battery connected to the system is disconnected. In this case, the charge in the capacitor remains constant and we shall use the energy equation in terms of charge and capacity. Of course the charge remains same and capacity increases by dielectric constant times. As a result, the total energy of the capacitor decreases by dielectric constant times.

In the second case, the dielectric material is placed and the battery is kept connected. As battery is still connected in the system, the voltage applied to the capacitor remains constant and its capacity increases by dielectric times. Thus here we shall use the energy stored in the capacitor in terms of capacity and voltage and hence total energy stored in the capacitor increases by dielectric constant times as shown below.


Problem and Solution

Here in the given problem number of capacitors are connected in parallel and their effective capacity is given. So that we can measure the individual capacity of the capacitor. Again it is given that the capacitors are connected in series and certain voltage is applied to the system. We need to measure the total energy stored in the system.

This can be done quite easily by first measuring the effective capacity of the system when they are connected in series. Then by applying the concept of energy stored in the capacitor, we can measure the energy as shown below.


Problem and Solution

This problem is not about capacity but rather about basic potential itself. A charged particle is moving under certain voltage and we need to measure the velocity acquired by it.

It can be solved quire easily using the concept of conservation of energy as shown below. The work done due to potential difference is actually converted into kinetic energy.


Problem and Solution

This problem is also not about capacity rather about electric potential and intensity. A charged particle of known mass is attached to a string and an electric field is applied to it. Now there is force to the field and gravitational force acting on the particle simultaneously. Thus the charged particle  turns an angle wit the vertical. We need to find the tension developed in the string and it can be done quite easily using the triangle law of vectors as shown in the diagram below.



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Capacitors in Series and parallel with Problems and Solutions

Capacitor is a device that is capable of storing energy and charge between its plates. We can connect the capacitors in different combinations.

Capacitors in Series

If one plate of the capacitor is connected to the other charged plate to the next capacitor and keep on connecting, this kind of connection is called series connection, When they are connected in series, the charge distribution on all of them is same but the total voltage connected to the system is shared across different capacitors basing on their capacity.

In series combination, total voltage of the system is the sum of all voltages shared across the system. We can find that the effective capacity of capacitors is less than any individual capacitors. It can be derived as shown below.



 Capacitors in Parallel

When capacitors are connected in parallel, the voltage shared across each capacitor is similar to the individual voltage on each capacitor. But the charge supplied to the system is shared across different capacitors based on their capacities.

If all positive plates of different capacitors are connected together and the negative plates of capacitors are also connected together, this kind of combination is called parallel combination.


When capacitors are connected they together can acquire a common potential as shown below. If different kind of plates are connected, the answer vary with the sign.


Problem and Solution

We know that when capacitors are connected in series, the effective capacity decreases and when they are connected in parallel, their effective capacity increases. If individual capacitors were need to be find out basing on total capacity of the systems when they are connected in series and parallel, we can find as shown in the problem below.


Problem and Solutions

When capacitors are connected in series, the charge across all the capacitors is same, but voltage is shared across them. We can find individual voltage as show in the diagram and problem with solution below.



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