From chapter electricity we know a little bit about electric field E⃗ and how it is produced at all points around it.
Likewise magnets produces magnetic field at all points round it.
We already learned about heating effects of electric current in previous chapter about electricity. Now in this chapter we shall study about another phenomenon related to current that is magnetic effects of current.
An electric current carrying wire behaves like a magnet:- So, we already know that an electric current-carrying wire behaves like a magnet. Let us now describe an experiment that shows the presence of magnetic field near a current carrying wire. ACTIVITY showing presence of magnetic field near current carrying wire:-
This experiment is also called Oersted Experiment.
First take a straight thick copper wire and place it between the points X and Y in an electric circuit, as shown in Fig. 1. Figure 1: compass needle is deflected when it is placed near a current carrying wire
Now we place a small compass near to this copper wire.
After placing the needle note the position of its needle.
Now insert the key into the plug to close the circuit and pass the current through the circuit.
Since the current is flowing in the circuit now observe the change in the position of the compass needle.
In the above activity we observed that the needle of the compass gets deflected when it is placed near the current carrying conductor. The result of this activity implies that current flowing through copper wire is producing a magnetic effect. Thus we can say that electricity and magnetism are linked to each other.
Who was Hans Christian Oersted? Hans Christian Oersted (1777-1851) through his experiments showed that electricity and magnetism are related to each other. His research later used in radio, television etc. The unit of magnetic field strength is name Oersted in his honour.
Magnets and magnetism
Magnets have been source of curiosity for ages. You can find magnets in places like laboratories, in toys, magnetic stickers that stick in refrigerator etc.
So, what is a magnet? The substances which have the property of attracting small pieces of iron, nickel and cobalt etc. are called magnets and this property of attraction is called magnetism.
Most of the metals like copper, gold, silver aluminium etc. are not attracted to magnets.
Magnets are found naturally in certain natural rocks and can also be made artificially by certain methods.
Artificially made permanent magnets are made in various shapes like bar, rod, disk, ring etc.
In a bar, rod and horse shoe magnets north and south poles are dictated by letters N and S or North Pole is indicated by a dot.
In disk and ring magnets one face is North Pole and another face is South Pole.
Permanent magnets are commonly used as a direction finding compass.
What are magnetic poles? Magnetic poles refer to the two areas of a magnet where the magnetic effects are the strongest. The poles are generally termed as the north and south poles.
Properties of magnet:
Attracts objects of iron, cobalt and nickel.
Force of attraction of a magnet is greater at its poles then in the middle.
Like poles of magnets repel each other while unlike poles of magnets attract each other.
A free suspended magnet always point towards north and south direction.
The pole of a magnet which points toward north direction is called North Pole or north seeking.
The pole of a magnet which points toward south direction is called South Pole or south seeking.
Magnetic Field
When we bring two magnets near each either they attract each other or they repel each other.
We can explain this force of attraction and repulsion between two magnets using the concept of Magnetic Field.
Magnets produces magnetic field in the space around it, which exerts force on any other magnet placed in this region. So it is the region around magnet within which its influence can be experienced.
What is magnetic Field? The space around a magnet in which the force of attraction and repulsion due to the magnet can be detected is called the magnetic field.
IMPORTANT NOTE:- Each point in the field of any magnet has a particular strength and magnetic field at each point has definite direction. How do you find the direction of the magnetic field due to magnet at a point near it? The direction of the magnetic field due to a magnet at a point near it can be found by placing a magnetic compass at that point. The compass needle gets deflected when it is placed near the magnet.
More about compass
The simplest compass is a magnetized metal needle mounted in such a way that it can spin freely.
Needle of a compass is a small bar magnet. This is the reason it gets deflected when we place it in the field of other magnet.
Compass needles are lightweight because earth has very week magnetic field. To show up the effect of that tiny magnetic field it should have even less effect due to gravity (note:- that gravitational force is much stronger then the force produced by earth’s magnetic field).
Compass needles are mounted on frictionless bearings because in this case there would be less frictional resistance for the magnetic force to overcome.
The ends of a compass needle points approximately in North and south directions.
About earth’s magnetism
The earth has a magnetic field which we call as the earth’s magnetic field.
The magnetic field is tilted slightly from the Earth’s axis.
The core of earth is filled with molten iron (Fe) which give Earth its very own magnetic field.
This large magnetic field protects the Earth from space radiation and particles such as the solar wind.
The region surrounding Earth where its magnetic field is located is termed as the Magnetosphere.
Earth has a magnetic field that has a shape similar to that of a large bar magnet.
To the north is the magnetic north pole, which is really the south pole of Earth’s bar magnet. (It is because this pole attracts the north pole of the compass magnet)
Magnetic Field Lines
Magnetic field surrounding the magnet and the force it exerts are depicted using imaginary curved lines with arrow called magnetic field lines.
Ways of obtaining magnetic field lines around a bar magnet
(A) Iron filings demonstration
Procedure:-
Fix a sheet of white paper on a drawing board using some adhesive material.
Place a bar magnet in the centre of it.
Sprinkle some iron filings uniformly around the bar magnet (Fig. 2). A salt-sprinkler may be used for this purpose.
Now tap the board gently.
Iron filings near the bar magnet align themselves along the field lines.
Fig. 2 Iron filings near the bar magnet align themselves along the field lines.This happens because the magnet exerts its influence in the region surrounding it. Therefore the iron filings experience a force. The force thus exerted makes iron filings to arrange in a pattern. The lines along which the iron filings align themselves represent magnetic field lines. (B) Demonstration using magnetic compass With this demonstration you can draw the field lines of a bar magnet yourself
Procedure of this activity:-
Take a small compass and a bar magnet.
Place the magnet on a sheet of white paper fixed on a drawing board, using some adhesive material.
Mark the boundary of the magnet.
Place the compass near the north pole of the magnet.
Here you will notice that the south pole of the needle points towards the north pole of the magnet. The north pole of the compass is directed away from the north pole of the magnet.
Mark the position of two ends of the needle.
Now move the needle to a new position such that its south pole occupies the position previously occupied by its north pole.
In this way, proceed step by step till you reach the south pole of the magnet as shown in Fig. 3. Fig. 3 Drawing a magnetic field line with the help of a compass needle.
Join the points marked on the paper by a smooth curve. This curve represents a field line.
Repeat the above procedure and draw as many lines as you can. You will get a pattern shown in Fig. 4. These lines represent the magnetic field around the magnet. These are known as magnetic field lines. Fig. 4 Field lines around a bar magnet
Observe the deflection in the compass needle as you move it along a field line. The deflection increases as the needle is moved towards the poles.
Observations
Direction in which compass needle points is the direction of the magnetic field.
The strength of the magnetic field is inversely proportional to the distance between the field lines.
Magnetic field lines never cross each other. It is unique at every point in space.
Magnetic field lines begin at the north pole of a magnet and terminate on the South Pole.
Properties of magnetic field lines
All field lines are closed curves.
Outside the magnet field lines emerge from North Pole and merge at South Pole.
Inside a magnet, the direction of field lines is from South Pole to its north pole.
Field lines never intersect each other.
Field lines are closed together near the poles and spread out away from them.
The field is stronger where the field lines are more closely spaced. So, the field is stronger near the poles then at other points.
Why do field lines never intersect each other? If two lines were to intersect each other, then a compass needle placed at the point of interaction would point in two different directions which is not possible.
We know about light and also know that light travels in a straight line path in a medium or two different mediums with same density.
Now a question arises what happens when light travels from one medium to another with different densities for example from air to glass.
When light ray is made to travel from one medium to another say from air to glass medium then light rays bend at the boundary between the two mediums.
So, the bending of light when it passes from one medium to another is called Refraction of light.
The refraction of light takes place on going from one medium to another because the speed of light is different in two media.
Medium in which speed of light is more is called optically rarer medium and medium in which speed of light is less is known as optically denser medium. For example glass is an optically denser medium than air and water.
NOTE:- When light goes from rarer medium to denser medium it bends towards the normal and when it goes from denser medium to rarer medium it bends away from the normal.
Refraction through a rectangular glass slab
To understand the refraction of light through a glass slab consider the figure given below which shows the refraction of light through a rectangular glass slab.
Here in this figure AO is the light ray travelling in air and incident on glass slab at point O.
Now on entering the glass medium this ray bends towards the normal NN’ that is light ray AO gets refracted on entering the glass medium.
After getting refracted this ray now travels through the glass slab and at point B it comes out of the glass slab as shown in the figure.
Since ray OB goes from glass medium to air it again gets refracted and bends away from normal N1N'1 and goes in direction BC.
Here AO is the incident ray and BC is the emergent ray and they both are parallel to each other and OB is the refracted ray.
Emergent ray is parallel to incident ray because the extent of bending of the ray of light at the opposite parallel faces which are PQ (air-glass interface) and SR (glass-air interface) of the rectangular glass slab is equal and opposite.
In the figure i is the angle of incidence, r is the angle of refraction and e is the angle of emergence.
Angle of incidence and angle of emergence are equal as emergent ray and incident ray are parallel to each other.
When a light ray is incident normally to the interface of two media then there is no bending of light ray and it goes straight through the medium.
Laws of refraction of light
Refraction is due to change in the speed of light as it enters from one transparent medium to another.
Experiments show that refraction of light occurs according to certain laws.
So Laws of refraction of light are
The incident ray, the refracted ray and the normal to the interface of two transparent media at the point of incidence, all lie in the same plane.
The ratio of sine of angle of incidence to the sine of angle of refraction is a constant, for the light of a given color and for the given pair of media. This law is also known as Snell’s law of refraction.
If i is the angle of incidence and r is the angle of refraction then sinisinr=constant=n (1) This constant value is called the refractive index of the second medium with respect to the first.
The Refractive Index
We now know about refraction of light and the extent of the change in direction that takes place in a given pair of media is expressed in terms of the refractive index, the "constant" appearing in equation 1.
The refractive index is related to an important physical quantity that is relative speed of propagation of light in different media as light propagates with different speeds in different media.
Consider the figure given below
Let v1 be the speed of light in medium 1 and v2 be the speed of light in medium 2 then the refractive index of medium 2 with respect to medium 1 is given by the ratio of the speed of light in medium 1 and the speed of light in medium 2. So, where n21 is the refractive index of medium 2 with respect to medium 1.
The refractive index of medium 1 with respect to medium 2 is represented as n12. It is given by
If medium 1 is vacuum or air, then the refractive index of medium 2 is considered with respect to vacuum. This is called the absolute refractive index of the medium.
If c is the speed of light in the air and v is the speed of light in any medium then refractive index nmof the medium would be
Refraction by Spherical Lenses
A lens is a piece of transparent glass bound by two spherical surfaces.
There are two types of lens
A convex lens bulges outward and is thick at the center and thinner at the edges. Convex lens converges the light rays as shown below in the figure 1(a). Hence convex lenses are called converging lenses.
A concave lens bulges inward and is thinner in the middle and thicker at the edges. Such lenses diverge light rays as shown in Figure 1(b) Such lenses are called diverging lenses.
A lens, whether it is a convex lens or a concave lens, has two spherical surfaces which form a part of a sphere. The centers of these spheres are called centers of curvature of the lens usually represented by the letter C.
Since there are two centers of curvature, we may represent them as C1 and C2.
An imaginary straight line passing through the two centers of curvature of a lens is called its principal axis as shown in figure 1.
The central point of a lens is its optical centre. It is usually represented by the letter O.
A ray of light through the optical centre of a lens passes without suffering any deviation.
The effective diameter of the circular outline of a spherical lens is called its aperture.
In figure 1 (a) you can see several rays of light parallel to the principal axis are falling on a convex lens. These rays, after refraction from the lens, are converging to a point on the principal axis. This point on the principal axis is called the principal focus of the lens.
Letter F is usually used to represent principal focus. A lens has two principal foci.
Similarly in figure 1 (b) several rays of light parallel to the principal axis are falling on a concave lens. These rays, after refraction from the lens, are appearing to diverge from a point on the principal axis. This point on the principal axis is called the principal focus of the concave lens.
The distance of the principal focus from the optical centre of a lens is called its focal length represented by letter f .
Image Formation by Lenses
Lenses form images by refraction of light and type of image formation depends on the position of the object in front of the lens.
We can place the objects at
Infinity
Beyond 2F1
At 2F1
Between F1 and 2F1
At focus F1
Between focus F1 and optical center O
Image formation by a convex lens for different positions of the object is shown below in the table
Position of the object
Position of the image
Relative size of the image
Nature of the image
Infinity
At focus F2
Highly diminished, point sized
Real and inverted
Beyond 2F1
Between F2 and 2F2
Diminished
Real and inverted
At 2F1
At 2F2
Same size
Real and inverted
Between F1 and 2F1
Beyond 2F2
Enlarged
Real and inverted
At focus 2F1
At infinity
Infinitely large or highly enlarged
Real and inverted
Between F1 and optical center O
On the same side of the lens as the object
Enlarged
Virtual and erect
Nature, position and relative size of the image formed by a concave lens for various positions of the object is given below in the table
Position of the object
Position of the image
Relative size of the image
Nature of the image
At infinity
At focus F
Highly diminished, point-sized
Virtual and erect
Between infinity and optical center O of the lens
Between F1 and optical center O
Diminished
Virtual and erect
A concave lens will always give a virtual, erect and diminished image, irrespective of the position of the object.
Image Formation in Lenses Using Ray Diagrams
Ray diagram helps us to study the nature, position and relative size of the image formed by lenses.
For drawing ray diagrams we first consider how light rays falling on both concave and convex lens in three different ways get refracted.
First consider the case for convex lens
Secondly consider the case for concave lens
The ray diagrams for the image formation in a convex lens for a few positions of the object are summarized below in the table
The ray diagrams for the image formation in a concave lens for a few positions of the object are summarized below in the table
Sign Convention for Spherical Lenses
All the distances are measured from the optical center of the lens.
The distances measured in the same direction as that of incident light are taken as positive.
The distances measured against the direction of incident light are taken as negative.
The distances measured upward and perpendicular to the principle axis are taken as positive.
The distances measured downwards and perpendicular to principle axis is taken as negative.
Lens Formula and Magnification
Lens Formula gives the relationship between object distance (u), image image-distance (v) and the focal length (f ) and is expressed as 1f=1v−1u This formula is valid in all situations for any spherical lens.
The magnification produced by a lens is defined as the ratio of the height of the image and the height of the object.
Magnification produced by a lens is also related to the object-distance u, and the image-distance v and is given by m=vu
The power of a lens is defined as the reciprocal of its focal length. It is represented by the letter P. The power P of a lens of focal length f is given by P=1f
Power of a convex lens is positive and that of a concave lens is negative.
The SI unit of power of a lens is ‘dioptre’. It is denoted by the letter D.
1 dioptre is the power of a lens whose focal length is 1 meter so, 1D=1m–1.
Physical phenomena associated with the presence and flow of electric charge is known as electricity. Electricity and electrical phenomenon have a lot of applications in our day to day life and they also gives a wide variety of well-known effects, such as lightning, static electricity, electromagnetic induction and the flow of electrical current.
Electricity occurs due to several types :
Electric charge: a property of some subatomic particles, which determines their electromagnetic interactions.
Electric current: a movement or flow of electrically charged particles, typically measured in amperes.
Electric field: an especially simple type of electromagnetic field produced by an electric charge even when it is not moving (i.e., there is no electric current). The electric field produces a force on other charges in its vicinity. Moving charges additionally produce a magnetic field.
Electric potential: the capacity of an electric field to do work on an electric charge, typically measured in volts.
In this chapter we will study about electricity.
Fractional electricity***
To understand electricity we need to understand the concept of electric charge first. Let us understand this concept using this example. When two dry substances of different types are rubbed together and are then separated , each substances acquires property of attracting light pieces of paper , dry leaves, straw etc. The substances being rubbed acquire something which give them this property. That something is called Fractional Electricity. The substances are said to have become charged after acquiring or loosing electric charge. The fractional electricity produced have been found to be of two types i.e., positive electricity (charge) and negative electricity (charge). The to substances rubbed together acquire equal and opposite charges.
Positive charge
Negative charge
Glass rod
Silk Cloth
Woolen cloth or cat skin
Amber, ebonite, rubber rod
Woolen carpet
Rubber shoe soles
Woolen coat
Plastic seat
2. Electric Charges
Electric charge is a fundamental property like mass; length etc. associated with elementary particles for example electron, proton and many more.
Electric charge is the property responsible for electric forces which acts between nucleus and electron to bind the atom together.
Charges are of two kinds
negative charge
positive charge
Electrons are negatively charged particles and protons, of which nucleus is made of, are positively charged particles. Actually nucleus is made of protons and neutrons but neutrons are uncharged particles.
Electric force between two electrons is same as electric force between two protons kept at same distance apart i.e., both set repel each other but electric force between an electron and proton placed at same distance apart is not repulsive but attractive in nature
All free charges are integral multiples of a unit of charge e, where e = -1.602 × 10 -19 C i. e., charge on an electron or proton.
Thus charge q on a body is always denoted by q = ne where n = any integer positive or negative
Unit of electric Charge
Charge on a system can be measured by comparing it with the charge on a standard body.
SI unit of charge is Coulomb written as C.
1 Coulomb is the charge flowing through the wire in 1 second if the electric current in it is 1A.
Charge on electron is -1.602 × 10 -19 C and charge on proton is positive of this value.
3. Conductors and insulators
There is a category of materials in which electric charges can flow easily while in other materials charges cannot flow easily.
Substances through which electric charges can flow easily are called conductors. All metals like copper, aluminum etc. are good conductors of electricity.
Substances through which electric charges cannot flow are called insulators.
Few examples of insulating materials are glass, rubber, mica, plastic, dry wood etc.
Presence or absence of free electrons in a material makes it a conductor or insulator.
Conductors have free electrons which are loosely held by nuclei of their atoms whereas insulators do not have free electrons as in insulators electrons are strongly held by nuclei of their atoms.
4. Electric potential and potential difference
Charges present in a conductor does not flow from one end to another on their own.
Electric charges or electrons move in a conductor only if there is a difference of electric pressure, called potential difference, along the conductor.
This difference of potential may be produced by a battery, consisting of one or more electric cells.
Potential difference across the terminals of the cell is generated due to chemical reaction within the cell.
When the cell is connected to a conducting circuit element, the potential difference sets the charges inside the conductor in motion and produces an electric current.
In order to maintain the current in a given electric circuit, the cell has to expend its chemical energy stored in it.
The potential difference between two points in an electric field is defined as the amount of work done in moving a unit positive charge from one point to another point. So,
The SI unit of electric potential difference is volt (V)
The potential difference between two points is said to be one Volt if 1 Joule of work is done in moving 1 Coulomb of electric charge from one point to another. Thus
The potential difference is measured by means of an instrument called the voltmeter.
The voltmeter is always connected in parallel across the points between which the potential difference is to be measured.
5. Electric current and electrical circuits
Consider two metallic conducting balls charged at different potential are hanged using a non-conducting insulating wires .Since air is an insulator ,no charge transfer takes place
Now if we join both the metallic wire using a conducting metallic wire then charge will flow from metallic ball at higher potential to the one at lower potential.
This flow of charge will stop when the two balls would be at the same potentials.
If somehow we could maintain the potential between the metallic balls through a cell or battery, we will get constant flow of the charge in metallic wire, connecting the two conducting balls
This flow of charge in metallic wire due to the potential difference between two conductors used is called electric current.
So, Electric current is expressed by the amount of charge flowing through a particular area in unit time.
In other words, it is the rate of flow of electric charges (electrons) in a conductor (for example copper or metallic wire).
If a net charge Q, flows across any cross-section of a conductor in time t, then the current I, through the cross-section is The S.I. unit of electric current is Ampere (A)
When 1 Coulomb of charge flows through a cross-section of conductor in 1 second then current flowing through the conductor is said to be 1 Ampere.
Current is measured by an instrument called ammeter. It is always connected in series in a circuit through which the current is to be measured.
A continuous and closed path of an electric current is called an electric circuit. For example figure given below shows a typical electric circuit comprising a cell, an electric bulb, an ammeter A and a plug key K. Note that the electric current flows in the circuit from the positive terminal of the cell to the negative terminal of the cell through the bulb and ammeter
The conventional direction of electric current is from positive terminal of the cell to the negative terminal through the outer circuit.
Or we can say that conventional direction of electric current is in the direction of the flow of positive charged carriers.
6. Circuit Diagrams
We already know that electric circuit is a continuous path consisting of cell (or a battery), a plug key, electrical component(s), and connecting wires.
Electric circuits can be represented conveniently through a circuit diagram.
A diagram which indicates how different components in a circuit have to be connected by using symbols for different electric components is called a circuit diagram.
Table given below shows symbols used to represent some of the most commonly used electrical components
7.Ohm's Law
Ohm's law is the relation between the potential difference applied to the ends of the conductor and current flowing through the conductor. This law was expressed by George Simon Ohm in 1826.
Statement of Ohm's Law If the physical state of the conductor (Temperature and mechanical strain etc.) remains unchanged, then current flowing through a conductor is always directly proportional to the potential difference across the two ends of the conductor Mathematically V ∝ I or V=IR where constant of proportionality R is called the electric resistance or simply resistance of the conductor.
Value of resistance depends upon the nature, dimension and physically dimensions of the conductor.
From Ohm's Law Thus electric resistance is the ratio of potential difference across the two ends of conductor and amount of current flowing through the conductor.
If a graph is drawn between the potential difference readings (V) and the corresponding current value (I), then the graph is found to be a straight line passing through the origin as shown below in the figure
From graph we see that these two quantities V and I are directly proportional to one another.
Also from this graph we see that current (I) increases with the potential difference (V) but their ratio V/I remain constant and this constant quantity as we have defined earlier is called the Resistance of the conductor.
Electric resistance of a conductor is the obstruction offered by the conductor to the flow of the current through it.
SI unit of resistance is Ohm (Ω) where 1 Ohm=1 volt/1 Ampere or 1Ω=1VA-1.
The resistance of the conductor depends
on its length,
on its area of cross-section
on the nature of its material
Resistance of a uniform metallic conductor is directly proportional to its length (l) and inversely proportional to the area of cross-section (A). That is, Where ρ is the constant of proportionality and is called the electrical resistivity of the material of the conductor.
The SI unit of resistivity is Ω m. It is a characteristic property of the material.
The metals and alloys have very low resistivity in the range of 10-8 Ω m to 10-6 Ω m. They are good conductors of electricity.
Insulators like rubber and glass have resistivity of the order of 1012 to 1017 Ω m.
Both the resistance and resistivity of a material vary with temperature.
8. Factors affecting of resistances of a conductor
Electric resistance of a conductor (or a wire) depends on the following factors
Length of the conductor: - From equation 5 we can see that resistance of a conductor is directly proportional to its length. So, when length of the wire is doubled, its resistance also gets doubled; and if length of the wire is halved its resistance also gets halved. Thus a long wire has more resistance then a short wire.
Area of cross-section:- Again form equation 5 we see that resistance of a conductor is inversely proportional to its area of cross-section. So, when the area of cross-section of a wire is doubled, its resistance gets halved; and if the area of cross-section of wire is halved then its resistance will get doubled. Thus a thick wire has less resistance and a thin wire has more resistance.
3. Nature of material of conductor:- Electrical resistance of a conductor also depends on the nature of the material of which it is made. For example a copper wire has less resistance then a nichrome wire of same length and area of cross-section.
4. Effect of temperature:- It has been found that the resistance of all pure metals increases on raising the temperature and decreases on lowering the temperature. Resistance of alloys like manganin, nichrome and constantan remains unaffected by temperature.
9. Resistance of a system of resistors
We know that current through a conductor depends upon its resistance and potential difference across its ends.
In various electrical instruments resistors are often used in various combinations and Ohm’s Law can be applied to combination of resistors to find the equivalent resistance of the combination.
The resistances can be combined in two ways
In series
In parallel
To increase the resistance individual resistances are connected in series combination and to decrease the resistance individual resistances are connected in parallel combination.
9(a) Resistors in Series
When two or more resistances are connected end to end then they are said to be connected in series combination.
Figure below shows a circuit diagram where two resistors are connected in series combination.
Now value of current in the ammeter is the same irrespective of its position in the circuit. So we conclude that " For a series combination of resistors the current is same in every part of the circuit or same current flows through each resistor "
Again if we connect three voltmeters one across each resistor as shown below in the figure 4.The potential difference measured by voltmeter across each one of resistors R1 , R2 and R3 is V1 , V2and V3 respectively and if we add all these potential differences then we get
This total potential difference V in equation 6 is measured to be equal to potential difference measured across points X and Y that is across all the three resistors in figure 3. So, we conclude that <"the total potential difference across a combination of resistors in series is equal to the sum of potential differences across the individual resistors."
Again consider figure 4 where I is the current flowing through the circuit which is also the current through each resistor. If we replace three resistors joined in series by an equivalent single resistor of resistance R such that, the potential difference V across it, and the current I through the circuit remains same.
Now applying Ohm’s law to entire circuit we get< On applying Ohm's law to the three resistors separately we have,< From equation 6 So here from above equation 9 we conclude that when several resistances are connected in series combination, the equivalent resistance equals the sum of their individual resistances and is thus greater than any individual resistance.
9(b) Resistors in parallel
When two or more resistances are connected between the same two points they are said to be connected in parallel combination.
Figure below shows a circuit diagram where two resistors are connected in parallel combination.
IMPORTANT NOTE
When a number of resistors are connected in parallel, then the potential difference across each resistance is equal to the voltage of the battery applied.
When a number of resistances are connected in parallel, then the sum of the currents flowing through all the resistances is equal to total current flowing in the circuit.
When numbers of resistances are connected in parallel then their combined resistance is less than the smallest individual resistance. This happens because the same current gets additional paths to flow resulting decrease in overall resistance of the circuit
To calculate the equivalent resistance of the circuit shown in figure 5 consider a battery B which is connected across parallel combination of resistors so as to maintain potential difference V across each resistor. Then total current in the circuit would be Since potential difference across each resistors is V. Therefore, on applying Ohm's Law Putting these values of current in equation 10 we have If R is the equivalent resistance of parallel combination of three resistors heaving resistances R1, R2and R3 then from Ohm's Law Or, Comparing equation (10) and (11) we get
For resistors connected in parallel combination reciprocal of equivalent resistance is equal to the sum of reciprocal of individual resistances.
Value of equivalent resistances for capacitors connected in parallel combination is always less than the value of the smallest resistance in circuit.
10. Heating Effect of current
When electric current passes through a high resistance wire, the wire becomes and produces heat. This is called heating effect of current.
This phenomenon occurs because electrical energy is gets transformed into heat energy when current flows through a wire of some resistance say R Ω.
Role of resistance in electrical circuits is similar to the role of friction in mechanics.
To we will now derive the expression of heat produced when electric current flows through a wire.
To we will now derive the expression of heat produced when electric current flows through a wire.
For this consider a current I flowing through a resistor of resistance R. Let V be the potential difference across it as shown in the figure 6
Let t be the time during which charge Q flows. Now when charge Q moves against the potential difference V , then the amount of work is given by Therefore the source must supply energy equal to VQ in time t. Hence power input to the circuit by the source is
The energy supplied to the circuit by the source in time t is P×t that is, VIt. This is the amount of energy dissipated in the resistor as heat energy.
Thus for a steady current I flowing in the circuit for time t , the heat produced is given by Applying Ohm's law to above equation we get This is known as Joule's Law of heating
According to Joule's Law of Heating , Heat produced in a resistor is (a) Directly proportional to the square of current for a given resistor. (b) Directly proportional to resistance of a given resistor. (c) Directly proportional to time for which current flows through the resistor.
11. Applications of heating effect of current
The heating effect of current is utilized in the electrical heating appliances for example electric iron, room heaters, water heaters etc.
The heating effect of electric current is utilized in electric bulbs or electric lamps for producing light.
An electric fuse is an important application of the heating effect of current. The working principle of a fuse wire is based on the heating effect of current. When high current flow through the fuse (current higher than the rated value) then the heat developed in the wire melts it and breaks the circuit.
In an electric heater one type of coil is used. A high resistance material like nichrome or same type of material is used as coil. The coil is wound in grooves on ceramic format or china clay. Flowing electric current through the coil it becomes heated. Due to high resistance the coil becomes red color forms.
12. Electric Power
Rate of doing work or the rate of consumption of energy is known as POWER Mathematically,
SI unit of power is Watt which is denoted by letter W. The power of 1 Watt is a rate of working of 1 Joule per second.So,
" the rate at which electric work is done or the rate at which electric energy is consumed is called electric power "
We will now derive formula for the calculation of electric power. From equation 14 we know that Now we know that work done W by current I when it flows for time t under a potential difference V is given by Putting this value of work done in equation 16 we get Hence, Electric Power = voltage x current
12 (a) Power in terms of I and R
From equation 17 we know that P=VI Now from Ohm's law Putting above equation in equation 15 we get
Above formula is used to calculate power when only current and resistance are known to us.
12 (b) Power in terms of V and R
From equation 17 we know that P=VI Now from Ohm's law Or we have
Putting this value of I in equation 15 we get
This formula is used for calculating power when voltage and resistance are known to us.
