write activity to prove Ohm's law
Answers
Set up a circuit shown in the below figure, consisting of a nichrome wire XY of length 0.5m, an ammeter, a voltmeter and 4 cells of 1.5V each.
First use only one cell as the source in the circuit. Note the reading in the ammeter I, for the current and reading of the voltmeter V for the potential difference across the nichrome wire XY in the circuit. Tabulate them in a table.
Next connect 2 cells in the the circuit and note the respective readings of the ammeter and voltmeter for the values of current through the nichrome wire and p.d across the nichrome wire
Repeat the above steps using 3 cells and then 4.
calculate the ratio of V to I for each pair of p.d V and current I.
Plot a graph between V and I.
You will observe that V is directly proportional to I
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 !!!