Question

state ohm's law and prove it

Answer 1

according to ohm's law, if a current l flows through a wire when potential difference across the ends of the wire is V, the resistance offered by the wire to the flow of current is the ratio of potential difference across it to the current flowing in it i. e., resistance of wire
=potential difference across the wire(V)/current flowing in the wire (l)
R=V/l or V=IR
resistance is a scalar quantity
unit of resistance:unit of potential difference /unit of current
1 ohm=1 volt/1 ampere

Answer 2

OHM'S LAW : Ohm's law states that the current flowing through a conductor is directly proportional to the potential difference applied across its ends.

PROOF :

This is the way of proving Ohm's law without calculus ❗

According to Joule, the amount of heat (H) produced in a resistor (a kind of conductor) is directly proportional to the square of the current (I), resistance (R) of the resistor or conductor and time (t) for which the current flows through the resistor or conductor.

Symbloically, H ∝ I²

H ∝ R and H ∝ t

By the rule of Joint variation, combining these three laws we get, H ∝ I²Rt

or, H = 1/J × I²Rt [Where, 1/J is the proportionality constant that Joule got experimentally. It can also be called as a experimental constant. ]

In S.I. system, the value of J is 1, i.e., J = 1 and hence, H = I²Rt

Also, W = J H

As I told earlier, J = 1 in S.I. system, hence :

W = H

=> W = I²Rt .....(i)

From the equation of potential difference between two points in an electric field, we can say that : V = W/Q or, W = VQ ....(ii)

So, from (i) and (ii), we can write that :

VQ = I²Rt

=> V × I × t = I² × R × t

=> V = I × R = IR

This equation V = IR is known as Ohm's law.

Proof without using Calculus !!!