The figure shows an experimental plot for discharging of a capacitor in an $R-C$ circuit. The time constant $\tau$ of this circuit lies between

  • A
    $100\; sec$ and $150\; sec$
  • B
    $150\; sec$ and $200\; sec$
  • C
    $0\; sec$ and $50\; sec$
  • D
    $50\; sec$ and $100\; sec$

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$A$ capacitor of capacity $0.1 \mu F$ connected in series to a resistor of $10 M \Omega$ is charged to a certain potential and then made to discharge through the resistor. The time in which the potential will take to fall to half its original value is (Given, $\log _{10} 2=0.3010$ ) (in $\,s$)

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