Heating Effect of Electric Current

Cause of Heating Effect

When potential is applied across the ends of a conductor, the free electrons move with drift velocity and current is established in the conductor. As the free electrons move through the conductor, they collide with positive ions of the conductor. On collision, the kinetic energy of an electron is transferred to the ion with which it has collided. As a result, the kinetic energy of vibration of the positive ion increases, i.e., temperature of the conductor increases. Therefore, as current flows through a conductor, the free electrons lose energy which is converted into heat. Since the source of e.m.f. (e.g., a battery) is maintaining current in the conductor, it is clear that electrical energy supplied by the battery is converted into heat in the conductor.

Heat produced in a conductor by electric current: Suppose a battery maintains of V volts across the ends of a conductor AB of resistance R ohms. Let the steady current that passes from end A to end B be I amperes. If this current flows for t seconds, then charge transferred from point A to B is q = It coulomb. The electric potential energy lost (W) by the charge q as it moves from A to B is given by;

W = charge × p.d. between A and B

= qV = V I t = I² R t ( V = I R)

or W = I² R t

This loss of electric potential energy of charge is converted into heat (H) because the conductor AB has resistance only.

H = I² R t Joules calories ...(i)

Eq. (i) is known as Joule's law of heating. It is because joule was the first scientist who studied the heating effect of electric current through a resistor. Thus according to Joule, heat produced in a conductor is directly proportional to

square of current through the conductor
resistance of the conductor
time for which current is passed

Note:

Electric Power

The power of an electric appliance is the rate at which electrical energy is converted into other forms of energy (e.g. heat, etc.). For example, a 60 W bulb converts 60 J of electrical energy into heat and light each second.

Thus referring to as the charge q (= I t) moves from point A to B, it loses electric potential energy = qV. In other words, q V joules of electrical energy is converted into heat in t seconds.

Electric Power or watt

Electric Power = V I watts ...(i)

= I² R watts ...(ii)

= V²/R watts ...(iii)

Any one of the three formulae can be used to calculate electric power, depending upon the problem at hand.

Unit of Electric Power

P = V I

The SI unit of p.d. is 1 V and that of current is 1 A so that SI unit of power = 1 V × 1 A = 1VA or 1 watt (1W).

Hence electric power of a circuit or device is one watt if a current of 1 A flows through it when a p.d. of 1V is maintained across it.

The bigger units of elecric power are kilowatt (kW) and megawatt (MW).

1kW = 100 W; 1MW = 10³kW = 10⁶W.

The commercial unit of power is horse power (H.P) where 1 H.P. = 746 W.

Note: Electric appliances are rated in terms of electric power. The faster the appliance converts electrical energy into some other form of energy, the greater the electric power it has. Thus, in 1 second, a 100 W bulb converts more electrical energy into heat and light then a 60 W bulb.

Electrical Energy

The loss of electrical potential energy in maintaining current in a circuit is called electrical energy consumed in the circuit.

Thus in above figure, as the charge q ( = I t) moves from point A to B, it loses electric potential energy = q V = V I t Joules. This loss of electric potential energy is converted into heat. We say that electrical energy consumed in t second is V I t Joules.

Electrical energy consumed,

W = V I t = I² R t

Unit of Electrical Energy

W = V I t = power × time

The SI unit of power is 1 W and that of time is 1s so that SI unit of electrical energy = 1W × 1s = 1Ws or 1J.

1J (or 1Ws) energy is consumed when a device (e.g., bulb, heater, etc.) converts electrical energy to other forms at a rate of 1W for a time of 1 second.

(Commercial Unit : In practice, electrical energy is measured in kilowatt-hour (kWh).

1kWh energy is consumed when a device converts electrical energy to other forms at a rate of 1kW for a time of 1 hour.)

Electrical energy in kWh = Power in kW × Time in hours

The electricity bills are made on the basis of total electrical energy consumed by the consumer. The unit for billing of electrical energy is 1kWh. Thus when we say that a consumer has consumed 100 units, it means that electrical energy comsumption is 100 kWh. Note that 1kWh is also called Board of Trade Unit
(B. O.T. U.) or unit of electricity.

Use of Power and Energy Formulae

It has already been discussed that electric power as well as electrical energy consumed can be expressed by three formulas. While using these formulae, the following points may be kept in mind;

(i) Electric Power,

Electrical energy consumed,

The above formulae apply only to resistors and to devices (e.g, electric bulb, heater, electric kettle etc.)

(ii) Electric power P = V I watts

Electrical energy consumed , W = V I t Joules

These formulae apply to any type of load including the one mentioned in point (i).

Efficiency of electric Device

The efficiency of an electric device is the ratio of useful output power to the input power i.e.,

Important Points

While dealing with problems on heating appliances, the following points should be kept in mind:

(i) The electrical energy in kWh can be converted to Joules by the following relation:

1 kWh = 36 × 10⁵ Joules

(ii) The heat energy in calories can be converted into Joules by the following relation:

1 cal = 4.18 J; 1 kcal = 4180 J

(iii) The electrical energy in kWh can be converted into calories (or kilocalories) by the following relation:

1 kWh = 860 kcal

(iv) The electrical energy supplied to the heating appliance form the input energy. The heat obtained from the device is the output energy. The difference between the two, if any, represents the loss of energy during conversion from electrical to heat energy.