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Electrostatic Potential And Capacitance

Question
CBSEENPH12039555

Let C be the capacitance of a capacitor discharging through a resistor R. Suppose t1 is the time taken for the energy stored in the capacitor to reduce to half its initial value and t2 is the time taken for the charge to reduce to one–fourth its initial value. Then the ratio t1/t2 will be

  • 1

  • 1/2

  • 1/4

  • 2

Solution

C.

1/4

straight U space equals space fraction numerator straight q squared over denominator 2 straight c end fraction
straight U space equals space straight U subscript max over 2
rightwards double arrow space straight q space equals space straight Q subscript straight o over straight v subscript 2
straight q space equals space straight Q subscript 0 straight e to the power of negative straight t divided by RC end exponent
In space straight q over straight Q subscript 0 space equals space minus straight t over RC semicolon
straight t space equals space RC space In straight Q subscript 0 over straight q
at space straight t subscript 1 space rightwards double arrow space straight q space equals space fraction numerator straight Q subscript 0 over denominator square root of 2 end fraction space straight t subscript 1 space equals space RC over 2 In space 2
at space straight t subscript 2 space rightwards double arrow space straight q space equals space straight Q subscript 0 over 4 space straight t subscript 2 space equals space 2 RC space In space 2
straight t subscript 1 over straight t subscript 2 space equals space 1 fourth

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