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
v_d=(eE/m)τ
but Now E=V/l
Therefore
v_d=(eV/ml)τ
Also I=neAv_d
Substituting the value of v_d 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
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
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