Chapter - 3

One ampere: 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

Note: current is measured by an instrument called ammeter and it is always connected in series of the circuit and has low resistance.

Direction of electric current: 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 law: 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 is depends on nature, length, area of cross section and temperature of the conductor. This equation can be written as follows

     R = V /I where , V = potential difference , I = current and R = resistance of conductor

The s.i. unit of resistance of is ohm denoted by the symbol ‘Ω’.

One ohm: 1 ohm is the resistance of a conductor such that when a potential difference of 1 volt is applied to its ends, a current of 1 ampere flows through it.

If we draw the graph b/w current and potential difference it will always a straight line. It is clear from the following graph

Good conductors, resisters and insulators:
On the basis of their electrical resistance, all the substance can be divides in to 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 having comparatively high electrical resistance are called resisters. Like the alloys nichrome , manganin and constantan, all have quit 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

    1. 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.

    Note: 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 series: 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                                       

     

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