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Electricity

Electricity Synopsis

Synopsis

 

Electric Charge

  • In metals, the moving charges are the free electrons constituting the current, while in electrolytes and ionised gases, positively charged ions (cations) and negatively charged ions (anions) are the moving charges which constitute current. 
  • If n electrons pass through the cross section of a conductor in time t, then the total charge passed through the conductor is given as Q = ne and current in conductor is given as,


    begin mathsize 12px style straight I equals straight Q over straight t equals ne over straight t end style 

Electric Current

  • The current is the rate of flow of charge across a cross-section which is normal to the direction of flow of current.

    begin mathsize 12px style Current space open parentheses straight I close parentheses space equals space fraction numerator Charge open parentheses straight Q close parentheses over denominator Time open parentheses straight t close parentheses end fraction end style
  • It is a scalar quantity.
  • Its SI unit is ampere (A). It is given as

    begin mathsize 12px style Unit space of space straight I equals fraction numerator Unit space of space straight Q over denominator Unit space of space straight t end fraction equals straight C over straight s equals straight A end style
  • Thus, current is one ampere if the rate of flow of charge is one coulomb per second.

Electric Potential

Concept of Potential 

  • A body released from a height always moves (falls) from a higher point to a lower point, that is from a point of higher gravitational potential to a point of lower gravitational potential.
  • If two containers are filled with water up to different levels, then irrespective of their size and shape, the water flows from a container containing water at higher level to the other container. This is due to difference in hydrostatic pressure in the two containers.



  • If two bodies at different temperatures are kept in contact, then irrespective of their size and shape the heat flows by conduction from the body at higher temperature to the body at lower temperature.
  • Similar analogy is applied to two charged conductors are joined by a metal wire.
  • The conductor with higher concentration of electrons is said to be at a lower potential and the conductor with lower concentration of electrons is said to be at a higher potential.
  • The electrons flow from a body at a lower potential to the body at a higher potential.
  • Potential is the electrical state of a conductor which determines the direction of flow of charge when the two conductors are either kept in contact or joined by a metallic wire.



  • The electric current flows from a body at a higher potential to the body at a lower potential, and this is called conventional current. This direction is opposite to the direction of flow of electrons which is called electronic current.

Concept of Potential Difference

  • The potential at a point is defined as the work done in bringing a unit positive charge from infinity to that point.

    begin mathsize 12px style Potential space difference equals fraction numerator Work space done over denominator Charge end fraction end style
  • If W is joule of work done in bringing a test charge Q coulomb from infinity to a point, then the potential V at the point is given as,

    begin mathsize 12px style straight V equals straight W over straight Q end style
  • The potential difference between two points is said to be 1 volt if the work done in bringing 1 coulomb of charge from infinity to the point is 1 joule.

    begin mathsize 12px style 1 space volt equals fraction numerator 1 space joule over denominator 1 space coulomb end fraction equals 1 space straight J space straight C to the power of negative 1 end exponent end style
  • The potential difference between two points is equal to the work done in moving a unit positive charge from one point to the other.

    begin mathsize 12px style straight V subscript straight A minus straight V subscript straight B equals straight W over straight Q end style
  • It is a scalar quantity. Its SI unit is also volt (V).

 

Concept of Resistance

  • There is always some obstruction in the current that flows through a conductor like a metal wire and this obstruction is called its electrical resistance.
  • The current in the circuit flows due to the drift of electrons. The metal wire has free electrons which move in random manner.
  • When the ends of wire are connected to a cell, the electrons start moving from negative terminal to the positive terminal. In this process they collide with the positive ions and due to this the speed of electrons decreases. Thus, the metal offers resistance to the flow of electrons because of these collisions.

 

The resistance of a conductor depends on four factors:

  • Length of the conductor: A long conductor offers more resistance because the number of collisions in it is more than a short conductor. Thus, the increase in the length of the conductor increases its resistance.
    Resistance (R) α length (l)
  • Thickness of the conductor: A thick conductor has less resistance because it allows an easy flow of electrons across its larger area of cross-section. Thus, the resistance of a conductor decreases with increase in thickness.
    begin mathsize 12px style Resistance space open parentheses straight R close parentheses space straight alpha space fraction numerator 1 over denominator Area space of space cross minus section open parentheses straight A close parentheses end fraction end style
  • Nature of the conductor: The resistance depends on the material of the wire as there is different concentration and different arrangement of atoms in different materials.
    Thus, resistance of wires of same lengths, same area of cross-section, but of different materials will be different.
    Good conductors like metals have low resistance. Insulators like glass have high resistance.
  • Temperature of the wire: A higher temperature of the wire causes the ions in it to vibrate more rapidly. As a result the number of collisions increases, and hence the resistance increases.
 
Ohm’s law
  • Ohm’s law states that, “the current flowing through a conductor is directly proportional to the potential difference V across its ends, provided the temperature and physical conditions of the conductor remain the same”.
    I α V

    begin mathsize 12px style straight V over straight I equals constant equals straight R end style
    V = IR
  • R is constant for a given metallic wire at a given temperature, and this constant is named as resistance. It is the property of a conductor to resist the flow of charges through it.
  • Its SI unit is ohm and is denoted as Ω.
  • If we plot the I-V graph for a conductor, then it shows a linear nature.



  • The slope of the graph is reciprocal of resistance of the conductor.


    begin mathsize 12px style Slope equals fraction numerator increment straight I over denominator increment straight V end fraction equals fraction numerator 1 over denominator Resistance space of space conductor end fraction end style

  • Conductance: It is defined as the reciprocal of resistance.

    begin mathsize 12px style Conductance equals fraction numerator 1 over denominator Resistance space end fraction end style
  • Hence, we can say that the slope of I.V graph gives the conductance of the conductor.

 

Ohm’s Law: Experimental Verification

  • The experimental setup for Ohm’s law is shown below.



  • First the key K is closed and the rheostat Rh is adjusted to get the minimum reading in the ammeter A and voltmeter V.
  • The sliding terminal of rheostat is then moved to increase the current gradually and each time the value of current I flowing in the circuit and the corresponding value of potential difference V across the resistance wire R, are recorded. In this way, different sets of values of V and I are recorded.
  • Then for each set of values of V and I, the ratio V/I is calculated.
  • A graph of V against I is plotted and its slope is calculated.



  • The slope from the graph is then obtained as,

    begin mathsize 12px style straight R equals fraction numerator increment straight V over denominator increment straight I end fraction equals Slope end style
  •  Greater the slope of the graph, greater is the resistance.

 

Specific Resistance or Resistivity

  • The resistance of a wire depends on the following factors:
    o Directly proportional to the length (l) of the wire.
    o Inversely proportional to the area of cross-section of the wire.
    o Nature of the material of wire.

    R α 1

    begin mathsize 12px style straight R space straight alpha space 1 over straight A equals 1 over πr squared
therefore straight R space straight alpha space 1 over straight A
straight R space equals space straight rho 1 over πr squared end style

  • Here, ρ is the constant of proportionality and is called the electrical resistivity or specific resistance of the material of the wire.
  • The resistivity will be given as,

    begin mathsize 12px style straight rho equals RA over straight I end style
  • If l = 1, A = 1, then ρ = R.
  • Thus, we define resistivity as the resistance of a wire of that material of unit length and unit area of cross section.
  • Its SI unit is ohm-metre (Ω m).
  • It depends on the material of the conductor and temperature.
  • Conductivity: The reciprocal of resistivity is called conductivity. It is represented by σ.


    begin mathsize 12px style straight sigma equals 1 over straight rho equals 1 over RA end style
  • Its SI unit is ohm-1 metre-1 or siemen metre-1.

 

Choice of Material of Wire

The choice of material of a wire depends on the purpose for which the wire is to be used. 

  • The wires which are used for electrical connections and for power transmission should possess negligible resistance, so they are made of material such as copper or aluminium, for which the resistivity is very small. Further they are made thick so that their resistance can be considered to be negligible.
  • The resistance wires (or standard resistors) are made of material such as nichrome, manganin, constantan, etc., for which the resistivity is quite large and the effect of change in temperature on their resistance is negligible. 
  • A fuse wire is made from an alloy of lead and tin because its resistivity is high and melting point is low. 
  • A wire made up of tungsten is used for filament of electric bulb because it has a high melting point and high resistivity. 
  • A nichrome wire is used as the heating element in appliances such as heater, toaster, oven etc. because the resistivity of nichrome is very high and increase in its value with increase in temperature is also high. 
 
Resistance in Series
  • When two or more resistors are joined from end to end, the resistances are said to be connected in series.



  • The current in series remains the same across all the resistors.
  • The potential difference is the sum of potential differences across all the individual resistors.

    V = V1 + V2 + V…… (1)
  • Let I be the current in the circuit.
  • On applying Ohm’s law to the entire circuit, we get

    V = IRs…… (2)
    here, Rs is the combined resistance of the circuit.
  • Now, applying Ohm’s law to individual resistances, we get

    V1 = IR1
    V2 = IR2…… (3)
    V3 = IR3
  • From equations (1), (2) and (3), we get
    IR= IR1 + IR2 + IR3
    ∴ R= R1 + R2 + R3 
    here, Rs is the resultant resistance.
  • Thus, the resultant resistance of a series combination of resistors is the sum of individual resistances.
  • The resultant resistance is greater than all the individual resistances.
 
Combination of Resistances
  • When two or more resistors are joined together with the same end, the resistances are said to be connected in parallel.



  • The potential difference in parallel remains the same across all the resistors.
  • The current is the sum of the currents across all the individual resistors.

    I = I1 + I2 + I3…… (1)
  • Let Rp be the resultant resistance of the circuit.
  • On applying Ohm’s law to the entire circuit, we get

    begin mathsize 12px style straight I equals straight V over straight R subscript straight P end style…… (2)
  • Now, applying Ohm’s law to individual resistances, we get

    begin mathsize 12px style straight I subscript 2 equals straight V over straight R subscript 1
straight I subscript 2 equals straight V over straight R subscript 2.......... open parentheses 3 close parentheses
straight I subscript 3 equals straight V over straight R subscript 3 end style

  • From equations (1), (2) and (3), we get

    begin mathsize 12px style straight I subscript 2 equals straight V over straight R subscript 1
straight I subscript 2 equals straight V over straight R subscript 2.......... open parentheses 3 close parentheses
straight I subscript 3 equals straight V over straight R subscript 3 end style

    here, Rp is the resultant resistance.
  • Thus, the reciprocal of resultant resistance of a parallel combination of resistors is the sum of reciprocals of individual resistances.
  • The resultant resistance is lesser than all the individual resistances.
 
Advantages and Disadvantages



 
 
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