Heating effect - SSLC physics chapter one

There are several devices which uses heating effect of electric current. For example electrical heater, In Normal heater coil is heated by passing current through it . Due to this heat,water inside the heater also getting heated. Another example is electric iron for ironing clothes. Here also heat is produced when current passes through a coil inside the electric iron. We can list few of the items uses heating effect of electric current.

Electric Heater

Electric Iron

Hair drier

Now let us analyse how this effect is produced. And try to develop mathematical equation for heat energy produced. So consider the circuit below.

circuit diagram

when the switch is closed , current will start flowing through the resistor. The voltmeter connected across the resistor will measure the voltage and the Ammeter connected in series will measure the current through it.

The current flowing through a material is the number of charges flowing per time.

Q = charge

t = time in seconds

we can state that " The potential difference applied will be 1V if one of work is required to move one coulomb of charge from one point to other."

We can also state this in different way .That is " One jule of work is required to move one coulomb of charge under potential difference of 1V."

That is , here the work is done by the voltage V. Voltage is doing the work of moving charge.

W = V W = Work ; V = voltage

For moving 1 coulomb charge ,

Work = V volts .

So for Q charge Work W = QV

Battery connected in the circuit is doing this work. So the power supplied by the Battery is

But

We know energy E = power(p) x time(t)

= p x t

= V I t

That is Energy supplied by the battery = V I t

This energy is converted to heat in the conductor. So we can say that,Heat energy developed in the conductor

${\color{Blue} H = VIt}$ ----------- 1

Using OHM'S LAW , We can formulate some more equations for Heat energy.
By Ohm's Law
$V=IR -------2$

$I=\frac{v}{R} -------3$

I = Current
R = Resistance

Substituting equation 2 in 1.

$H=IRIt= {\color{Blue} I^{2}Rt}$

Similarly ,Substituting equation 3 in 1

$H=V\frac{V}{R} t= {\color{Blue} \frac{v^{2}}{R}t}$

So far we got 3 equations for Heat .Those are