Question

A constant current i is passed through a resistor. Taking the temperature coefficient of resistance into account, indicate which of the plots shown in the figure best represents the rate of production of thermal energy in the resistor.
Figure

Answer 1

Plots which represents the rate of production of thermal energy in the resistor is: plot (d).

Explanation:

• It is to be understood that when there is a flow of current via the resistor, then the resistor’s temperature increases due to the production of heat, which is shown as $H=I^{2} R t$

where I is the current,

t is the current flowing time,

R is the resistor’s resistance.  

• The resistor’s resistance also increases with the increase in the resistor’s increase. The rate of thermal energy production in a circuit resistor is shown as:

dUdt = ddt(i2Rt) = i2R,

where R is the resistor’s resistance and i is current flowing through the resistor

R = resistance of the resistor.

• The resistance is directly proportional to the rate of thermal energy production. So, when there is resistance’s increase, dUdt also linearly increases, which is signified by plot d.