(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.
(a) When an electric charge Q moves against a p.d. V, the amount of work done is given by
W = Q x V .........(1)
we know, current, I = \(\frac{Q}{t}\)
Q = I x t ..........(2)
By ohm's law, \(\frac{V}{I}\) = R
V = I x R .........(3)
Putting eqn. (2) and (3) in eqn. (1),
W = I x t x I x R
W = I2Rt
Assuming that all the electrical work done is converted into heat energy, we get
Heat produced, H = I2Rt joules
This relation is known as Joule's law of heating.
(b) Given: P = 12W, V = 12V, t = 60 sec
P = VI
I = \(\frac{P}{V}\) = \(\frac{12}{12}\) = 1A
V = IR
R = \(\frac{V}{I}\) = \(\frac{12}{1}\) = 12 ohms
H = I2Rt
H = 12 x 12 x 60
H = 720 J
(c) The heat produced by the heater will become one-fourth because heat produced is directly proportional to the square of the current.
(d) When an electric current is passed through a high resistance wire, the wire becomes very hot and produces heat. This effect is knows as heating effect of current. This effect is used in room heaters and electric ovens.
(e) Tungsten is used for making the filaments of an electric bulb.