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QPage 196: Q9: HC Verma: Concepts of Physics - Volume 2 Electric Current in Conductors Page 196: Q9 Solution: The thermal energy developed in a current-carrying resistor is…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often treat $U=i^2Rt$ and $U=Vit$ as giving contradictory proportionalities because they ignore that $V$ and $R$ are not independent of $i$; you must state which quantity (voltage or resistance) is held constant before concluding $U\propto i^2$ or $U\propto i$.

The thermal energy developed in a current-carrying resistor is given by

U = i^2 Rt

and also by

U = Vit

. Should we say that

U

is proportional to

i^2

or

i

?

Step-by-Step Verified Solution

**Answer:**

U

is proportional to

i^2

when

R

is constant. It is proportional to

i

only when

V

is constant (which implies

R

changes). **Step-by-Step Explanation:**

U = i^2Rt

shows

U \\propto i^2

for a fixed resistor.

U = Vit

shows

U \\propto i

for a fixed voltage. The two expressions are consistent because

V = iR

; if

i

changes,

V

also changes (for fixed

R

). The question of proportionality depends on which quantities are held constant [citation:3].

All Questions in this Chapter

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