When a RC circuit is connected to a battery, what fraction ofthe battery voltage

Question

When a RC circuit is connected to a battery, what fraction ofthe battery voltage appears across the capacitor after two timeconstants: a) When the capacitor is charging from zero voltage? b) When discharging the capacitor from a fully chargedcondition? When a RC circuit is connected to a battery, what fraction ofthe battery voltage appears across the capacitor after two timeconstants: a) When the capacitor is charging from zero voltage? b) When discharging the capacitor from a fully chargedcondition?

Explanation / Answer

a)When the capacitor is charging from zero voltage,then V = Vo* e(-t/RC) When t = 2RC,then V = Vo* e(-2RC/RC) or V = Vo* e(-2) or V = Vo* (1/e2) or V = Vo* (1/(2.71)2) or V = 0.13 * Vo b)When discharging the capacitor from a fully chargedcondition,then V = Vo* (1 - e(-t/RC)) When t = 2RC,then V = Vo* (1 - e(-2RC/RC)) or V = Vo* (1 - 1/e2) or V = Vo* (1 - 0.13) or V = 0.87 * Vo b)When discharging the capacitor from a fully chargedcondition,then V = Vo* (1 - e(-t/RC)) When t = 2RC,then V = Vo* (1 - e(-2RC/RC)) or V = Vo* (1 - 1/e2) or V = Vo* (1 - 0.13) or V = 0.87 * Vo

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