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=(ne^{2}Aτ/ml) V (7)
or
V/I=(ml/ne^{2}Aτ)=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 [ML^{2}T^{-3}A^{-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
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