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Current Electricity and its Effects
Ohm’s Law gives a relationship between current and potential difference. Ohm’s law states that at constant temperature, the current flowing through a conductor is directly proportional to the potential difference across its ends. Thus, according to Ohm’s law,
Resistance of a Conductor
The property of a conductor due to which it opposes the flow of current through it is called resistance. The resistance of a conductor is numerically equal to the ratio of potential difference across its ends to the current flowing through it, i.e.,
Factors on which Resistance of a Conductor Depends
The resistance of a conductor depends on the following factors:
i) Length of the conductor
ii) Area of cross-section of the conductor (or thickness of the conductor)
iii) Nature of the material of the conductor
iv) Temperature of the conductor.
R µ l/A l = length of the conductor
A = cross-sectional area of the condcutor
R =r l/A ....(iii)
Where, r (rho) is a constant known as resistivity (or specific resistance) of the material of the conductor. The SI unit of resistivity is ohm-metre (W m).
Now in relation (iii), if we put A = 1, and l = 1, we get r = R
Thus, the resistivity of material of conductor is defined as the resistance of the conductor of unit length and unit area of cross-section.
Note: The resistivity of a substance does not depend on its length or thickness. It depends only on the nature and temperature of the substance.
Electrical resistivities of some substances at 20°C are given in the following table:
From the above table we find that
Resistivity of Metal < Resistivity of alloys < Resistivity of Insulators
Thus, the metals and alloys have very low resistivity in the range of 10–8 to 10–6 W m. They are good conductors of electricity.
For example, copper and aluminium metals are generally used for electrical transmission lines. Tungsten metal is used almost exclusively for filaments of electric bulbs. This is because tungsten has high melting point and does not oxidise (or burn) easily at high temperatures.
The resistivity of alloys is generally higher than that of its constituent metals. Also alloys do not oxide readily at high temperature
The resistivity of alloys is generally higher than that of its constituent metals. Also alloys do not oxide readily at high temperature.
For example, Manganin (alloy of copper, manganese and nickel) and constantan (alloy of copper and nickel)
are used to make resistors (resistance wires) used in electrical appliances.
Nichrome (an alloy of nickel, chromium, iron and manganese) is used for making the heating elements of electrical appliances like electric iron, room heaters, toaster, immersion rod, etc.
Note: The resistivity of semi-conductors like silicon and germanium is in between those of conductors and insulators and decreases on increasing the temperature.
Combination of Resistances (or Resistors)
There are two methods of joining the resistors together (i) in series and (ii) in parallel.
Resistors in Series
When two (or more) resistances are connected end to end consecutively, they are said to be connected in series.
Let three resistances R1, R2 and R3 are connected in series which is shown in the figure.
Thus,weThus,theirequivalentoreffective resistance isgivenby
Thus, we conclude that when several resistors are joined in series, the resistance of the combination Rs
equals to the sum of their individual resistances.
Resistors in Parallel
When two (or more) resistances are connected between the same two points, they are said to be connected in parallel.
Let us consider the arrangement of three resistors joined in parallel as shown in the figure.
Thus we conclude that the reciprocal of the combined resistance of a group of resistances connected in parallel is equal to the sum of the reciprocals of all the individual resistances.
Note: When a number of resistances are connected in parallel, then their combined or equivalent resistance is alwasys less than the smallest individual resistance.
Advantages of Connecting Electrical Appliances in Paralll
- i) In a series combination, when one component fails, the circuit is broken and none of the components in the circuit work But in parallel combination if one component fails, the working of other components will not be affected.
- ii) In a series circuit the current is constant throughout the electric circuit. So, it is impracticable to connect electric bulb and an electric heater in series, because they need currents of different values to operate properly. On the other hand, a parallel circuit divides the currents through the electrical gadgets and this is helpful when each gadget has different resistance and requires different current to operate properly.
The rate of which electric energy is dissipated (or consumed) is called electric power. The electric power P
is given by
Thus, the power is said to be 1 watt when an electrical appliance consumes electrical energy at the rate of
1 joule per second.
Other units of electric power used for commercial purposes are kilowatt and megawatt.
1 kilowatt (1kW) = 103 W
1 megawatt (1 MW) = 106 W
Formula for Calculating Electric Power
As we known that
Now, if we put, V = 1 volt and I = 1 ampere in equation (iii), we get electric power of 1 watt.
i.e., Power = 1 watt = 1 volt × 1 ampere or 1 watt = 1 VA
Thus, the power consumed by an electrical appliance is said to be 1 watt when 1 ampere of current is operated at a potential difference of 1 volt.
We know that Electric power = work done by electric current / time taken
Now, according to law of conservation of energy,
work done by electric current = Electric energy consumed
Power, P = W / t
or W = P × t or E = P × t.
Commercial Unit of Electrical Energy
For commercial purpose we use a bigger unit of electrical energy which is called kilowatt-hour (kWh).
One kilowatt-hour is the amount of electrical energy consumed when an electrical appliance having a power rating of 1 kilowatt is used for 1 hour.
1 kWh = 1000 W × 60 × 60 seconds
= 1000 joules/seconds × 3600 seconds
= 3600000 joules
= 3.6 × 106 J
Heating Effect of Electric Current
Whenever the electric current is passed through a metallic conductor, it becomes hot after some time. This indicates that the electrical energy is being converted into heat energy. This effect is known as heating effect of current.
Cause of Heating Effect of Current
When a potential difference is applied across the ends of a conductor, an electric field is set up across its ends. A large number of free electrons present in the conductor get accelerated towards the positive end and acquire kinetic energy due to which an electric current flows through the conductor. These accelerated electrons on their way suffer frequent collisions with the ions or atoms of the conductor and transfer their gained kinetic energy to them. As a result of this, the average kinetic energy of vibration of the ions or atoms of the conductor rises and consequently the temperature of the conductor rises. Thus the conductor gets heated due to the flow of electric current through it.
Heat Produced in a Conductor
Consider a conductor AB connected to cell as shown in the figure. Let V be the potential difference applied across the ends of AB and I be the current flowing through AB in time t.
Now, by definition of potential difference
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