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BITSAT2019PhysicsCapacitanceActual

A charged capacitor of capacitance C is discharging through a resistor of resistance R . At what time the charge on the capacitor is equal to one half of its initial value?

Options

  1. AR C 2
  2. BR C log e 2
  3. CR C log e   2
  4. D1 R C log e 2

Correct answer

C. R C log e   2

Step-by-step solution

The charge on the capacitor at time t in a discharging circuit is given by q = q 0 e - t / τ where, τ = R C = time constant ∴ q = q 0 e - t / R C when,    q = q 0 2 then q 0 2 = q 0 e - t / R C 1 2 = e - t / R C Taking natural log on both side log e 1 2 = log 0 e - t / R C - log e 2 = - t R C log e e ⇒ t = R C log e 2

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