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Electricity is an important source of energy in the modern time. It is used in our homes, factories and in transport. For example, it is used in our homes for lighting, operating fans and heating purposes. In industries it used for running many machines and in transport it is used to pull electric trains. It has been founded by the experiments that there are two types of charges- positive charge and negative charge. By convention, the charge acquired by the glass rod is called positive charge and charge acquired by an ebonite rod is called negative charge. An important property of electric charge is following:
1. Opposite charges attract each other. For example, a positive charge attracts negative charge. 2. Similar charges repel each other. For example a positive charge repel each other. For example a positive charge repel the another positive or negative charge repel the other negative charge.
The S.I. unit of electric charge is coulomb which is denoted by the letter 'C'. One coulomb can be define as follow :
One coulomb is that quantity of electric charge which exert the force of 9 x 109 N on an equal charge placed at a distance of 1 m from it. We will now know that all the matter containing the positive charge called protons and having negative charge called electrons. a proton possesses a positive charge of 1.6 x 10-19 C whereas the electron have a negative charge of 1.6 x 10-19 C.
Note: the s.i. unit of electric charge ‘coulomb’ is equivalent to the charge contained in 6.25 x 1018 electrons.
Conductors: those substances through which electricity can flow are called conductors. All the metals like silver, copper, aluminium etc are conductors. The metal alloys such as nichrome, manganin and constantan are also conductor of electricity but their conductivity is much less than that of pure metals. Carbon in the form of graphite is also good conductor of electricity and the human body is also good conductor.
Insulators: those substance in which the electric current cannot flow are called insulators. Glass, ebonite rubber, most plastics, paper, dry wood, wood, cotton, mica, Bakelite, and dry air are all insulators because they do not allow electric charges to flow through them. In the case of charged insulator like glass, ebonite etc.. the electric charges remain bound to them, and do not move away. We have just seen that some of the substance are conductors whereas others are insulators. All the conductors have electrons which are loosely held by the nuclei of their atoms. These electrons are known as , ‘free electrons’. And can move from one place to another throughout the conductors.
- The presence of “free electrons” in a substance makes it a conductor.
The electrons present in insulators are strongly held by the nuclei of their atoms. Since there are no “free electrons” in an insulator which can move from one place to another, an insulator does not allow electric charges to flow through it.
Electricity can be classified into two parts:
1. Static electricity: The electric charge in it do not move, Means it remains at rest. 2. Current electricity: The electric charge in it move from one place to another.
Electric potentialItalic text: the electric potential at a point in an electric field is defined as the work done in moving unit positive charge form infinity to that point. It is denoted by volt (V).
One voltItalic text: a potential of 1 volt at a point means that 1 joule of work is done in moving 1 unit of electric charge from infinity to that point. Potential differenceItalic text: the potential difference b/w two points in an electric current is defined as the amount of work in moving a unit charge from one point to other point.
Potential difference = work done / quantity of charge moved
If w joules of work has to be done move Q coulombs of charge from one point to another point, then the potential difference V b/w the points is given by the formula:
V = W/Q where
W = work done and Q = quantity of charge
The S.I. unit of potential difference is volt. The potential difference b/w two points is said to be 1 volt if one joule of work is done in moving 1 coulomb of electric charge from one point to the other. Thus, 1 Volt = 1 joule/ 1 coulomb
1 V = 1 /C
NoteItalic text: The potential difference is measured by means of an instrument, which has high resistance, called voltmeter and it always connected in parallel across the points where the potential difference is measured.
Electric CurrentItalic text: The flow of electric charges (electrons) in a conductor such as wire is called electric current. The magnitude of electric current in a conductor is the amount of electric charge passing through a given point of the conductor in one second. If a charge of Q coulomb flows through the conductor in t seconds, then the magnitude of the electric current(I) flowing through it, is given by
Current ( I )= Q /t
The S.I. unit of current is ampere which is denoted by the letter ‘ A’.
One ampereItalic text: when one coulomb of charge flows through any cross section of a conductor in one second, the electric current flowing through it will be one ampere. That is
1 ampere = 1 coulomb / 1 second or 1 A = 1C / 1s
A smaller unit of current is called “ milliampere” is also used, which is denoted by ‘mA’.
1 mA = 10-3 A and 1 micro ampere = 10-6 A
NoteBold text: Electric current is measured by an instrument called ammeter and it is always connected in series in the circuit and has low resistance.
Direction of electric currentItalic text: The conventional direction of electric current is from positive terminal to negative terminal through the outer circuit means in the opposite direction of movement of electrons in circuit.
Ohm’s lawItalic text: It gives a relationship b/w current and potential difference.
According to this, at constant temperature, the current flowing through a conductor is directly proportional to the potential difference across its ends.
If I is the current flowing through a conductor and V is the potential difference across its ends then according to ohm’s law:
I α V
Or V α I
Or V = R x I
where R is called “resistance” of the conductor.
The value of this constant depends on the nature, length, area of cross section and melting point of the conductor.
This equation can also be written as:
R = V /I
where , V = potential difference , I = current and R = resistance of conductor
The S.I. unit of resistance is ohmItalic text denoted by the symbol ‘Ω’.
One ohmItalic text: 1 ohm is the resistance b/w the two points of a conductor, when a constant potential difference of 1 volt, is applied to its ends, generates an electric current of one ampere in the conductor.
If we draw the graph b/w current and potential difference it will always a straight line.`
Good Conductors, Resistors and InsulatorsItalic text:
On the basis of their electrical resistance, all the substance can be divided into three groups:
# Good Conductors,
# Resistances and
# Insulators.
Those substances which have very low electrical resistance is called conductors. Like gold, silver, copper etc.
Those substances which have comparatively high electrical resistance are called resistors. Like the alloys nichrome , manganin and constantan, all have quite high resistance so they known as resistances.
And those substances which have infinite high electrical resistance are called insulators. An insulator does not allow electricity to flow from it. Rubber is an excellent insulator. Wood and paper are also insulator of electricity.
Factors affecting the resistance of a conductor:
The electrical resistance of a conductor depend upon the following factors: • Effect of length of conductor: on increasing the length of wire its resistance increases and on decreasing the length of wire the resistance will reduce. Actually, the resistance of wire is directly proportional to its length. • Effect of area of cross section of conductor: it has been found that the resistance of a conductor is inversely proportional to the area of the cross section of conductor which is used in the circuit. • Effect of nature of material of conductor: the electrical resistance of a conductor depends on the nature of its material which is it made. • Effect of temperature: the resistance of conductor of pure metals increases o increasing the temperature and decreases on decreasing the temperature.
Resistivity: It has been found that
1. The resistance of a given conductor is directly proportional to its length
R α l
2. The resistance of given conductor is inversely proportional to the area of cross section that is
R α 1/A
Then R α l/A
R = ρ x l/ A
Where (ρ) rho is a constant known as resistivity of the material of the conductor. And
R= resistance of the conductor and A is the area of cross section of conductor which is used in circuit.
From here ; resistivity (ρ) = Rx A / l
So, the s.i. unit of resistivity is ohm – meter or Ωm.
NoteItalic text: we use copper aluminium wires for the transmission of electricity because these have low resistivity. And the resistivity of alloys are much more higher than the pure metals.
Combination of resistances: The resistances can be combined in two ways (i) in series and (ii) in parallel Resistances in series: when two resistances are connected end to end consecutively, they are said to be connected in series and when two resistors are connected b/w the same twp points, they are said to be connected in parallel.
Resistances in seriesItalic text: According to the law of combination of resistances in series: the combined resistance of any number of resistances connected in series is equal to the sum of the individual resistances. For example, if a number of resistances R1, R2, R3.... etc are connected in series, then their combined resistance R is given by
R = R1+ R2+ R3.... Before we derive the formula for the resultant resistance of a number of resistances connected in series, we should keep in mind that:
1. When a number of resistances connected in series are joined to terminal of a battery, then each resistance has a different potential difference across its ends but the total potential difference across the ends of all resistances in series is equal to the voltage of the battery. Thus, when a number of resistances are connected in series, then the sum of the potential difference across all the resistances is equal to the voltage of the battery applied. 2. When a number of resistances are connected in series, then the same current flows through each resistanec.
Resultant resistance of two resistances connected in series:
If there are two resistances R1 and R2 connected in series. A battery of V volt has been applied to the ends of this series combination. Now suppose the potential difference across the resistance R1 is V1 and resistance R2 is V2. We have applied a battery of voltage V, so the total potential difference across the two resistances should be equal to the voltage of the battery That is : V = V1 + V2 --------------(1) We have just seen that the total potential difference due to the battery is V. Now suppose the total resistance of the combination be R, and the current flowing through the whole circuit be I. So by applying the ohm’s law
V/I = R or V = I R
Since the same current I is flows through both the resistances R1 and r2 connected in series, so by changing ohm’s law to both resistances , we will get
V1 = I R1, and V2 = I R2
Now putting the value of V1 and V2 in equation (1)
I X R = I X R1 + I X R2 or we get R = R1 + R2
Resistances in parallel: The combine resistance of a number of resistances connected in parallel can be calculated by using the law of combination of resistances in parallel. According to this law : the reciprocal of the combined resistance of a number of resistances connected in parallel is equal to the sum of the reciprocals of all the individual resistances. If a number of resistances R1, R2, R3.... etc are connected in paralle then the total resistance R of the combination is given by the formula
1/ R = 1/ R1 + 1/R2 + 1/R3....
Note: when a number of resistances are connected in parallel then their combined resistance is less than the smallest individual resistance.
Before we drive a formula for the resistance of a number of resistances connected in parallel, we should keep in mind that:
1. When a number of resistances are connected in parallel, then the potential difference across each resistance is the same which is equal to the voltage of the battery applied.
2. When a number of resistances connected in parallel are joined to the terminals of battery, then different amount of current flow through each resistance, but the current flowing through all the individual parallel resistances, taken together, is equal to the current flowing in the circuit as a whole. Thus, when a number of resistances are connected in parallel, then the sum of the currents flowing through all the resistances is equal to the total current flowing in the circuit.
Combine resistance of two resistances connected in parallel: If two resistances R1 and R2 are connected in parallel to one another b/w the same point A and B. A battery of V volts has been applied across the ends of this combination. In this case the potential difference across the ends of the both resistances will be the same. And it will be the equal to the voltage of the battery used. The current flowing through the two resistances in parallel is, however not the same Suppose the total current flowing in the circuit is I, then the current passing through R1 is I1 and R2 is I2 respectively. Then total current in the circuit
I = I1 + I2 .....................(i)
We know by ohm’s law I = V/R then
Since the potential V across both the resistance R1 and R2 in parallel is the same, so by applying ohm’s law to each resistance separately we get
I1 = V / R1 and I2 = V / R2
Now putting teh values if I1 and I2 in equation (i)
V/R = V / R1+ V / R2 and we get
1/ R = 1/R1 + 1/ R2
Domestic electric circuits: series or parallel : When designing an electric circuit, we should consider whether a series or parallel circuit is better for the intended use: for example, if we want to connect a large number of electric bulbs for decorating buildings and trees as during festivals such as Diwali or marriage function, then the series circuit is better because all bulbs connected in series can be controlled with just one switch. A series circuit is also safer because the current in it smaller. But there is a problem with this circuit. This is because if one bulb gets fused, then the circuit breaks and all the bulbs are turned off. An electrician has to spend a lot of time in locating the fused bulb form among hundreds bulbs, so as to replace it and restore the lighting.
The parallel electric circuit is better for connecting bulbs in house because then we can have separate switches for each bulb and hence operate it separately. In addition to having ease of operation, parallel domestic circuits have many other advantages over the series circuits.
Disadvantages of series circuit s for domestic wiring:
There are some following disadvantages of series circuits in the domestic wiring:
1. In series circuit, if one electrical appliance stops working due to some defect, then all other appliances also stop working. 2. In series, all the electrical appliances have only one switch due to which they can’t be turn off or on separately. 3. In series circuit, the appliances do not get the same voltage as that of the power supply line. 4. In the series connection of electrical appliance, the overall resistance of the circuit increases too much due to which the current from the power supply is low. Advantages of parallel circuits in domestic wring:
There are some following advantages of parallel circuits in the domestic wiring:
1. In parallel circuits, if one electrical appliance stop working due to some effect then all other appliances keep working normally. 2. In parallel circuit, each electrical appliance has own switch due to which it can be turn off or on independently, without effecting other appliances. 3. In parallel circuits, each electrical appliance gets same voltage as that of the power supply line. 4. In the parallel connection of electrical appliances, the overall resistance of the house hold circuit is reduced due to which the current from the power supply is high. Electric power:
we know that the rate of doing work is known as power, so electric power is the electrical work done per unit. That is
Power = work done / time taken
Or P = W/ t
Unit of power: The s.i. unit of electric power is watt denoted by the letter W, the power of 1 watt is a rate of working of 1 joule per second. That is
1 Watt = 1 joule / 1 second
Watt is a small unit, therefore, a bigger unit of electric power called kilowatt is used for commercial purpose. That is
One kilo watt = 1000 watts
1 kW = 1000 watts or 103 watts
So we can say that electric power is the rate at which electrical energy is consumed or electric ower is the electrical energy consumed per second. We can write down the another definition of electric power, when electric appliance is consumes electrical energy at the rate of 1 joule per second, its power is said to be 1 watt. We know that
Power = work done / time taken
Or p = W /t ---------------------(i) But we know that the work done W by current I when it flows for time t under a potential difference V is given by
W = V x I x t
Put this value in equation (i), we get
P = (V x I x t)/ t
P = V X I watts
Where, V = potential difference and I = current in amperes
Electric power = potential difference X current
The power expanded in heating a resistor or turning a motor depends upon the potential difference b/w the terminals of the device and electric current passing through it.
Power p = V x I watts
Now if an electrical appliance is operated at a potential difference of 1 volt and the device carries a current of 1 ampere, then power becomes 1 watt. That is
1 watt = 1 volt X 1 ampere
1 w = 1 V A means
One watt is the power consumed by an appliance which when operated at a potential difference of 1 volt carries a current of 1 ampere. Some other formulae of calculating the electric power: We have just obtained a formula for calculating electric power ; which is
P = V X I
We have other formulae of electric power which are following; 1. Power in term of I and R We have , P = v x I-----------------------(I) Now from ohm’s law we have V/I = R Or v = I X R , now from 1 P = I2R where , I = current and R = resistance 2. Power in the terms V and R P = V x I -------------------- (i) Also from ohm’s law we have V/I = R or I = V/R Putting this value of I in equation (i)’ we get P = V2/R , where V = potential difference and R = resistance of wire Note: power is inversely proportional to the resistance of wire. Power- voltage rating of electrical appliance:
We know that every electrical appliance like an electric an electric bulb , radio or fan has a label or engraved plate on it which tells us voltage and electric power consumed by it. For example, if we look at a particular bulb in our home, it may have the figures 100 w – 220 V written on it. Now 100w means this bulb has a power consumption of 100 w and 220 V means that it is to used on a voltage of 220 volts. The power rating of an electrical appliance tells us the rate at which electrical energy is consumed by the appliance.
For example: the power rating of 100 w on the bulb means that it will consume electrical energy at the rate of 100 joules per second. An electrical formula for calculating electrical energy: We have already studied that;
Electric power = work done by electric current / time taken
Now according to the law of conservation of energy, Work done by electric current = electric energy consumed Power = electric energy/ time Electric energy = power x time or E = P x t
The electrical energy consumed by an electrical appliance is given by the product of its power rating and the time for which it is used.
From this we conclude that the electrical energy consumed by an electrical appliance depends on two things 1. Power rating of the appliance and 2. Time for which the appliance is used In the formula: electrical energy = power x time, if we take the power in ‘watts’ and time in ‘ hours’ then the electrical energy becomes ‘watt – hours’. (Wh) One watt – hour is the amount of electrical energy consumed when an electrical appliance of 1 watt is used for one hour. Now we have describe the commercial unit of electrical energy of electrical energy called kilowatt – hour. One kilowatt – hour is the amount of electrical energy consumed when an electrical energy consumed when an electrical appliance having power rating of 1 kilowatt is used for 1 hour.
Relation b/w kilowatt – hour and joule: One kilowatt – hour is the amount of electrical energy consumed when an electrical energy consumed when an electrical appliance having power rating of 1 kilowatt is used for 1 hour. That is; 1 kilo watt – hour = 1 kilo watt for one hour
= 1000 watts for 1 hour
But : 1 watt = 1 joule / 1 second
1 kilo watt – hour = 1000 joules / second for one hours and one hour = 3600 seconds
Or 1 kilo watt hour = 36,00, 000 joules = 3.6 x 10 6 joules Note : kilowatt – hour is the “unit” of electrical energy for which we pay the electricity. Heating effect of current: When an electric current is passed through a high resistance wire like nichrome wire, the resistance wire becomes hot and produced heat. This is known as heating effect of current. The role of resistances in the circuits is same as the friction in the machines. Since a conductor, say a resistance wire, offers resistance to the flow of the current, so work must be done by a current continuously to keep itself flowing. We will calculate the work done by a current I when it is passing through a resistance R for time t. Now when an electric charge Q moves against a potential difference V, the amount of work done is given by
W = Q X V
From the definition of the current we have, I = Q /t or Q = I t
And from ohm’s law, we have V/ I = R or potential difference , V = I x R
Now putting Q = I x t and V = I x R We have W = I2 X R x t or Heat produced, H = I2 X R x t joules It is clear that the heat produced in a wire is directly proportional to 1. Square of current 2. Resistance of wire 3. Time for which current is passed Applications of the heating effect of current: The important applications of the heating effect of electric current are following o The heating effect of current is utilised in the working of electrical heating appliance such as electric iron, kettle, toaster, Oven, room heaters and water geysers. o The heating effect of current is utilised in electric bulb for producing light. o The heating effect of current is utilised in electric fuse for protecting house hold wiring and appliances.