After two time constants, the capacitor in an RC circuit is charged to what percentage of the supply voltage?
β’ Time constant (Ο) in an RC charging circuit β’ Exponential charging equation for a capacitor: Vc = Vs(1 β e^(βt/Ο)) β’ Relationship between multiples of Ο (1Ο, 2Ο, 3Ο, etc.) and the percentage of final voltage reached
β’ Write the standard formula for capacitor voltage during charging and substitute t = 2Ο into it. What expression do you get? β’ Evaluate the exponential term e^(β2). Approximately what decimal value do you obtain, and what percentage of the supply voltage does that correspond to? β’ Compare your calculated percentage with the choices given. Which one is closest to your computed result?
β’ Be sure you are using the charging formula (1 β e^(βt/Ο)), not the discharging one (e^(βt/Ο)). β’ Confirm that you correctly convert the decimal result to a percentage (multiply by 100). β’ Double-check the approximate value of e^(β2) before matching it to the answer choices.
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