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) Consider a resistor of Resistance R. Let the current flowing through the resistor be I and the potential difference across its ends be V.
In time t, let Q amount of charge flows through the resistor.

Work done on Moving charge will be,
$W=V\times Q$ ---------(1).

According to the definition of electric current,
$Q=I\times t$ -----------(2).

Putting equation (2) in (1),
$W=V\times I\times t$
And the work done is dissipated as heat.
Therefore,
Heat produced, $H=W=V\times I\times t=VIt$
$H=VIt$
According to Ohm's law $V=I\times R$
Putting this in equation (2), we get,
$H=IR\times It$
Therefore, $Heat=I^{2}Rt$

b) $H=I^{2}Rt=H=V\times I\times t$------- (1)

$P=V\times I$ ----------(2)

Substituting the value of (2) in (1)
$H=P\times t$
$H=12\times 60$

$H=720J$

c) If the current passing through an electric heater has been halved then the heat produced will also be reduced to one fourth.

Joules heating is given by, $H=I^{2}Rt$

H is the heat produced, I is the current through the wire of resistance R for time t.

If I is halved, i.e., $I=\frac{I}{2}$, then

$H=I^{2}Rt$ = $(1/2{)}^{2}Rt$ = $\left(1/4\right)Rt$

$H=\left(Rt/4\right)$

Therefore, heat produced will also be reduced to one fourth

d) The phenomenon of production of heat in a resistor by the flow of an electric current through it is called the heating effect of electric current. Two applications of the heating of current are:

(i). Directly proportional to the resistance.

(ii) Amount of current flow through the conductor

e) A metal named tungsten is used in making the filament of a bulb