Question

prove and state ohms laws mathematically​

Answer 1

Answer:

the current passing through a wire is directly proportional to potential difference across the end of the wire and resistance of the wire provided all physical conditions like temperature pressure remain same

this is called ohms law

Mathematical expression is

V=IR

hope you found this helpful!

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 !!!