When an electric current is passed through a conductor, heat is produced in the conductor because of the resistance to the flow of current. This effect is called the heating effect of electric current which is discussed below.
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Cause of Heating
When a potential difference 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., the 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. is maintaining current in the conductor, it is clear that electrical energy supplied by the source is converted into high temperature in the conductor. This high temperature is the result of the heating effect of electric current.
Heat Produced in a Conductor by Electric Current
The heating effect of electric current is studied by Joule, he found that the amount of heat produced (H) when current I amperes flows through a conductor of resistance R ohms for time t seconds is H = I2Rt joules. This equation is known as Joule’s law of heating.
Suppose a source maintains a potential difference of V volts across the ends of a conductor AB of resistance R ohms as shown in Figure.
Let the steady current that passes from A to B be I amperes. If this current flows for t seconds, then the charge transferred from A to B in t seconds is q = It
The electric potential energy lost (W) by the charge q as it moves from A to B is given by;
W = Charge × Potential difference between A and B
= qV = (It) V = I2Rt (since, V = IR)
or W = I2Rt
This loss of electric potential energy of charge is converted into heat (H) because the conductor AB has resistance only.
H = W = I2Rt joules = I2Rt / 4.18 calories = V2 t / R* 4.18 calories
It is found experimentally that 1 cal = 4.18 J.
The above equation 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
(i) square of current through the conductor
(ii) resistance of the conductor
(iii) time for which current is passed through the conductor.
Important points.
While dealing with problems with the heating effect of electric current, the following points may be kept in mind :
(i) The electrical energy in kWh can be converted into 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 calorie = 4·186 joules
1 kcal = 4186 joules
(iii) The electrical energy in kWh can be converted into calories (or kilocalories) by the following relation:
1 kWh = 36 × 105 joules = 36*105/4.186 calories = 860 * 103 calories = 1 kWh = 860 kcal.
(iv) The electrical energy supplied to the heating appliance forms 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 into heat energy.
Mechanical Equivalent of Heat (J)
Joule performed a series of experiments to establish the relationship between the mechanical work done and heat produced during the studies of the heating effect of electric current. He found that heat produced (H) is directly proportional to the amount of mechanical work done (W) i.e.,
H ∝ W or W = JH, where J is a constant of proportionality and is called the mechanical equivalent of heat. The value of J is 4·2 J/cal.
Note that J is a numerical factor relating mechanical units to heat units. To interpret the meaning of J, it takes 4·2 J of mechanical work to raise the temperature of 1g of water by 1°C. In other words, 4·2J of mechanical energy is equivalent to 1 calorie of heat energy.
Further, it may be noted that any loose connection gives rise to the resistance R, which in turn results in high temperatures in the joints of the conductors, promoting the heating effect of electric current. Therefore, the tightness of joints and connections must be securely checked where unnecessary heating is not desirable to reduce the heating effect of electric current.
