Question

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?

Answer 1

Answer:

$P=I^{2} R$

This relation is known as joules law of heating.

Explanation:

According to the definition of power dissipation if we neglect the power factor then,relation between power dissipation,potential difference and current is

$P=VI$..............(1)

According to ohm's law potential difference is directly proportional to current provided resistance remains same.

So, V=IR....................(2)

From (1) we get

$P=IRI$

$P=I^{2} R$

This power dissipation is known as heat produced in the conductor.

This relation is known as joules law of heating.

Answer 2

Answer:(a) When an electric charge Q moves against a p.d. V, the amount of work done is given by

W=Q×V                           ---------------(1)

We know,  current , I=

t

Q

​

Q=I×t                                ------------(2)

By ohm's law ,  

I

V

​

=R

V=I×R                             --------------(3)

Putting eqs. (2) and (3) in eq. (1),

W=I×t×I×R

W=I

2

Rt

Assuming that all the electrical work done is converted into heat energy , we get

Heat produced , H=I

2

Rtjoules

This relation is known as Joule's law of heating.

(b) Given : P=12W,V=12V,t=60sec

using the equation of power

P=VI

I=P/V=12/12=1A

The Ohm's law states that

V=IR

R=V/I=12/1=12ohm

The formula for heat is:

H=I

2

Rt

H=1

2

×12×60

H=720J

Explanation:(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 known 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.