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Ohm's Law & resistance<





Ohm's Law and Resistance


  • 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 α I
    or
    V=IR                    (6)
    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
  • Ohm's Law can be deducted using drift velocity relation as given in equation -3 .Thus from the equation
    vd=(eE/m)τ
    but Now E=V/l
    Therefore
    vd=(eV/ml)τ
    Also I=neAvd
    Substituting the value of vd in I relation
    I=(ne2Aτ/ml) V                    (7)
    or V/I=(ml/ne2Aτ)=R a constant for a given conductor
    Thus
    V=IR
    Mathematical expression of Ohm's Law
    From Ohm's Law
    V=IR or R=V/I                    (8)
    Thus electric resistance is the ratio of potential difference across the two ends of conductor and amount of current flowing through 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
  • Dimension of resistance is [ML2T-3A-2]

Current Voltage relations & Limitations


  • We know that current through any electrical device such as resistors depends on potential difference between the terminals
  • Devices obeying ohm's law follow a linear relationship between current following and potential applied where current is directly proportional to voltage applied .Graphical relation between V and I is shown below in figure


    Current voltage relation of resistor obeying ohm's law

  • Graph for a resistor obeying ohm's law is a straight line through the origin having some finite slope
  • There are many electrical devices that does not obey the ohm's law and current may depends on voltage in more complicated ways.Such devices are called non-ohmic devices for examples vacuum tubes,semiconductor diodes ,transistors etc
  • Consider the case of a semi conductor junction diode which are used to convert alternating current to direct current and are used to perform variety of logic functions is a non=ohmic device
  • Graphical voltage relation for a diode is shown below in the figure

    Current voltage relation of semiconducting diode

  • Figure clearly shows a non linear dependency of current on voltage and diode clearly does not follow the ohm's w
  • When a device does not follow obey ohm's law,it has non linear voltage -current relation and the quantity V/I is no longer a constant however ratio is still known as resistance which now varies with current
  • In such cases we define a quantity dV/dI known as dynamic resistance which expresses the relation between small change in current and resulting change in voltage
  • Thus for non-ohmic electrical devices resistance is not constant for different values of V and I


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