Question

(a) Derive the expression for the heat produced due to a current 'I' flowing for a time interval 't' through a resistor 'R' having a potential difference 'V' across its ends. With which name is this relation known?
(b) How much heat will an instrument of 12 W produce in one minute if it is connected to a battery of 12 V?
(c) The current passing through a room heater has been halved. What will happen to the heat produced by it?
(d) What is meant by the heating effect of current? Give two applications of the heating effect of current.
(e) Name the material which is used for making the filaments of an electric bulb.

Answer 1

(a) Since a conductor offers resistance to the flow of current, some work must be done by the current continuously to keep itself flowing. When an electric charge, Q moves against a potential difference, V, the amount of work done is given by:
W = Q x V (1)

From the definition of current, we know that:
Current, I = $\frac{Q}{t}$
So, Q = I x t (2)

And from Ohm's law, we have:
$\frac{\mathrm{V}}{\mathrm{I}}=\mathrm{R}$
or V = I x R (3)

Now, substituting Q = I x t and V = I x R in equation (1), we get:
W = I x t x I x R
So, the work done, W = I² x R x t

Assuming that all the electrical work done is converted into heat energy:
Heat produced = Work done in the above equation
Thus heat produced, H = I² x R x t joules
This is known as Joule's law of heating.

(b) Given: Power rating (P) = 12 W
Time interval (t) = 1 minute = 60 s (1 minute = 60 seconds)
Potential difference (V) = 12 V
Heat = I²Rt
But, we know that P = I²R
Therefore, H = P x t = 12 W x 60 s = 720 joules

(c) The heat produced by the room heater will become one-fourth the previous quantity when the current passing through it is halved because the heat produced is directly proportional to the square of the current.

(d) When an electric current is passed through a high resistance wire, like nichrome wire, the resistance wire becomes very hot and produces heat. This is called the heating effect of current.
The heating effect of current is used in electric irons, electric heaters, electric ovens, filament bulbs etc. and it is also utilised in electric fuses.

(e) Tungsten is used for making the filament of an electric bulb.