Question

derivation of heating effect of electric current

Answer 1

The resistance, R of the conductor. A higher resistance produces more heat

The time, t for which current flows. The longer the time the larger the amount of heat produced

The amount of current, I. the higher the current the larger the amount of heat generated.

To calculate the heat produced in a conductor, consider current I is flowing through a conductor AB of resistance R for time t. also consider that the potential difference applied across its two ends is V.

Now, total amount of work done in moving a charge q from point A to B is given by:

W=q×V

Now, we know that charge = current × time

q = I× t

V = I × R

Putting the values of q and V in equation (1), we get

W = (I × t) (I×R)

W= I²Rt

Now, assuming that all the work done is converted into heat energy we can replace symbol of ‘work done’ with that of ‘heat produced’. So,

H     =     I²RT

Answer 2

When a current flows through a conductor, heat energy generates in the conductor. Joule's law of heating gives the required formula for the heat produced as:-

H = $I^{2} .R.t$

It states that:-

• Directly proportional to the square of electric current flowing through it.

• Is directly proportional to the resistance of the conductor.

• Directly proportional to the time for which electric current flows through the conductor.

To derive above formula

Amount of work done in moving a charge against a potential difference is given by W = V.Q                    .....(i)

We know that V = I.R as per Ohm's law     ....(ii)

And that Q = I.t

or I = $\frac{Q}{t}$         .....(iii)

Putting value from (ii) ad (iii) in (i)

We get

W = (I.R).(I.t)

W = $I^{2} .R.t$

This work done is convereted into the heat energy. Here I is current in Ampere units, R is resistance in ohms and t is time in seconds. H is the amount of heat produced in Joules (J).