Home › ISC Class 12 › Physics › Current Electricity › The electric current across a cross-section of a…
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_
Related questions
For a battery of emf ε and internal resistance r driving current I through external resistA galvanometer of resistance G is converted into a voltmeter reading full-scale voltage V A galvanometer of resistance G shows full-scale deflection at current I_g. To convert it iThe relation between current density j, drift velocity v_d, number density n and charge e A wire has a resistance R. It is stretched uniformly so that its length becomes 2L. The neKirchhoff current law at a junction is a statement ofTwo cells of emf ε and internal resistance r each are connected in parallel. The equivalenA potentiometer of length L is used to compare emfs. If the balance lengths for cells of e