Ohm’s law states that the current flowing through a conductor is directly proportional to the potential difference across the conductor. The proportionality constant is the resistance of the conductor, it is a constant for a known temperature range.
An activity:
Connect the wires as shown in the diagram. Increase the rheostat to increase the current in the circuit, obtain the value of current in the circuit by the ammeter and also find the potential difference using the voltmeter. For increase in current see the brightness of the bulb connected. Use your knowledge so far to obtain the resistance of the bulb.
Graph of Ohm’s law is a straight line obtained when current in the circuit (I) is plotted along x axis and potential (V) along y axis.
Current is given by -----------1.
Current I = current, n = no. of electrons per unit volume, A = CSA of the conductor, v = drift velocity, e = electronic charge, E = Electric Field strength, = mass of electron, F = force, a = acceleration
------------2.
Again, Potential (V) is given by
------------3.
By 2 and 3
--------4.
where l = length of the conductor
Normally, due to electric force the charges should accelerate, but it does not accelerate due to repeated collisions with the +ve kernels. The path between two successive collision is called the free path ( Thus the charges have an average velocity called drift velocity v.
Thus, is given by,
where t = average relaxation time (i.e. free time without a collision)
Or, -----------5.
By 4 and 5
------------6.
By 1 and 6
Now mass of electron m, length of the conductor l, charge of electron e, CSA of conductor A, relaxation time t (constant for a given temperature). Thus
VαI (T remaining constant)
Which is Ohm's law