Question

The thermal energy developed in a current-carrying resistor is given by U = i2 Rt and also by U = Vit. Should we say that U is proportional to i2 or i?

Answer 1

The thermal energy (U) developed in a current-carrying resistor is proportional to $i^{2}$.

Explanation:

• In the expression U=Vit, voltage (V) and current i are variables for given time interval. So, based on this expression we cannot say that U is directly proportional to i.  

• In the expression $U=i^{2} R t$, the resistance (R) is fixed for the given circuit for a given time of interval and cannot be varied.

• So from this we can say that the thermal energy (U) is directly proportional to $i^{2}$ not i.