Question 250: Electrostatics & Capacitance

Question

A capacitor is discharging through a resistor R. Consider in time t
1
, the energy stored in the capacitor reduces to half of its initial value and in time t
2
, the charge stored reduces to one eighth of its initial value. The ratio t
1
/t
2
will be

Accepted Answer

For a discharging capacitor when energy reduces to half the charge would become $${1 \over {\sqrt 2 }}$$ times the initial value.
$$ \Rightarrow {\left( {{1 \over 2}} ight)^{1/2}} = {e^{ - {t_1}/	au }}$$
Similarly, $${\left( {{1 \over 2}} ight)^3} = {e^{ - {t_2}/	au }}$$
$$ \Rightarrow {{{t_1}} \over {{t_2}}} = {1 \over 6}$$

Answer

1/2

Answer

1/3

Answer

1/4

Answer

1/6

Electrostatics & Capacitance

A capacitor is discharging through a resistor R. Consider in time t 1 , the energy stored in the capacitor reduces to half of its initial value and in time t 2 , the charge stored reduces to one eighth of its initial value. The ratio t 1 /t 2 will be

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