Answer :

When current passes through a resistor, the heat produced by Joule’s heating effect is given by-




where,


I = current


R = resistance of the resistor


t = time for which current is flowing


Since with increase in the temperature of the resistor, its


resistance is also increased.


The rate of production of thermal energy in the resistor will be-



where


i = current flowing through the resistor and


R = resistance of the resistor


From above equation, the rate of production of thermal energy in


the resistor is directly proportional to the resistance.


Since, due to the heat generated by the resistance the operating temperature of the resistance increases given by the formula below:


R=Ro(1+αT)


Where


Ro is the initial resistance of the resistor


α is the coefficient of thermal conductivity


T is the temperature


Thus, the resistance of the resistor start increasing with the increase in temperature.


From the graph,


also increases linearly with time starting from a point , which is best shown by plot d.


Thus, option D is the correct option.

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