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Capacitor question

2019 · 12 Jan · Shift 2 · Q47
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Capacitor question

2019 · 12 Jan · Shift 2 · Q47

JEE MainPhysicsCapacitorMCQ+4 / −1
The charge on a capacitor plate in a circuit, as a function of time, is shown in the figure : JEE Main 2019 (Online) 12th January Evening Slot Physics - Capacitor Question 122 English When is the value of current at t = 4 s ?
  1. A
    zero
  2. B
    1.5 μ\muμ A
  3. C
    2 μ\muμ A
  4. D
    3 μ\muμ A
View written solutionFree

Correct answer: A

  1. Use the relation between charge and current

    Current is the rate of change of charge with time: i=dqdti = \frac{dq}{dt}i=dtdq​

    So, from a graph of charge qqq vs time ttt, the current at any instant is equal to the slope of the graph at that time.

  2. Read the graph at t=4 st=4\,\text{s}t=4s

    From the given qqq-ttt graph, at t=4 st=4\,\text{s}t=4s the graph is horizontal (slope is zero).

    Therefore, dqdt∣t=4 s=0\left.\frac{dq}{dt}\right|_{t=4\text{ s}} = 0dtdq​​t=4 s​=0

  3. Hence the current is

    i(4 s)=0i(4\text{ s}) = 0i(4 s)=0

  4. Check options

    • A: zero ✅
    • B: 1.5 μA1.5\,\mu\text{A}1.5μA ❌
    • C: 2 μA2\,\mu\text{A}2μA ❌
    • D: 3 μA3\,\mu\text{A}3μA ❌

So the correct option is A.

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