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The electric current across a cross-section of a conductor is defined as the net charge passing per unit time. Which expression correctly defines the instantaneous current?
A$I(t) = \lim_{\Delta t \to 0} \dfrac{\Delta Q}{\Delta t}$
B$I(t) = \lim_{\Delta t \to 0} \dfrac{\Delta t}{\Delta Q}$
C$I(t) = \lim_{\Delta Q \to 0} \dfrac{\Delta Q}{\Delta t}$
D$I(t) = \lim_{\Delta t \to 0} (\Delta Q \cdot \Delta t)$
Answer & Solution
Correct answer: A. $I(t) = \lim_{\Delta t \to 0} \dfrac{\Delta Q}{\Delta t}$
1. Current is the rate of flow of charge across a cross-section.
2. For a small charge $\Delta Q$ crossing in time $\Delta t$, the average current is $\Delta Q/\Delta t$.
3. The instantaneous current is the limit as $\Delta t \to 0$: $I(t) = \lim_{\Delta t \to 0} \dfrac{\Delta Q}{\Delta t}$.
4. So A is correct.
_Source: NCERT Class 12 Physics Ch 3 "Current Electricity", p.1_
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