Question

derive the equation for joules law of heating ​

Answer 1

When current is passed through a resistance some work is done.In a passive resistance the work done is equal to the amount of heat evolved in a resistance.



Consider a battery having terminal p.d ‘V’ is connected with a resistance as shown in figure. Let ‘I’ be the amount of current in the circuit. Let ‘q’ be the charge passed through the resistance in time‘t’ second.

We  know that,

Current (I)=Charge (q)Time (t)Current (I)=Charge (q)Time (t)

q = It……(i)q = It……(i)

If the potential difference between A and B is V. Then,

V = IR……(ii)V = IR……(ii)

Let ‘W’ be the amount of work done to move ‘q’ amount of charge through the resistance.

 So, Electric potential(V)=Workdone (W)q  So, Electric potential(V)=Workdone (W)q 

 or, W = qV or, W = qV

 W=VIt……(ii) W=VIt……(ii)

Now, from equation (i) and (ii)  and (iii),

W = It.IRW = It.IR

or, W = I2 RTor, W = I2 RT

Heat produced, H= RT  joule

In CGS system,

H=I2RTJCalH=I2RTJCal$

Answer 2

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Derivation of Joules's Law of Heating. When current is passed through a resistance some work is done.In a passive resistance the work done is equal to the amount of heat evolved in a resistance. ... Let 'W' be the amount of work done to move 'q' amount of charge through the resistance.