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https://texercises.com/exercise/half-life-and-time-constant/
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Exercise:
abcliste abc Calculate the time constant and the half-life for an RC circuit with a CaO capacitor and a RaO resistor. abc An RC circuit with a RbO resistor has a half-life of ThbO. Calculate the capacitance. abc The voltage across the capacitor in an RC circuit with a CcO capacitor drops to one percent of the initial value within TcO. Calculate the time constant and the resistance. abcliste

Solution:
abcliste abc tau taaF RatimesCa taa approx resulttaaP- T_/ tau ln ThaF RatimesCatimesln Tha approx resultThaP- abc C fractauR CbF fracThbRbtimes ln Cb approx resultCbP- abc The time to drop to one percent of the initial value is given by T_/ tau ln It follows for the resistance R fractauC RcF fracTcCctimesln Rc approx resultRcP abcliste
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Exercise:
abcliste abc Calculate the time constant and the half-life for an RC circuit with a CaO capacitor and a RaO resistor. abc An RC circuit with a RbO resistor has a half-life of ThbO. Calculate the capacitance. abc The voltage across the capacitor in an RC circuit with a CcO capacitor drops to one percent of the initial value within TcO. Calculate the time constant and the resistance. abcliste

Solution:
abcliste abc tau taaF RatimesCa taa approx resulttaaP- T_/ tau ln ThaF RatimesCatimesln Tha approx resultThaP- abc C fractauR CbF fracThbRbtimes ln Cb approx resultCbP- abc The time to drop to one percent of the initial value is given by T_/ tau ln It follows for the resistance R fractauC RcF fracTcCctimesln Rc approx resultRcP abcliste
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Branches
Direct Current
Tags
capacitor, exponential decay, half-life, time constant
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Difficulty
(1, default)
Points
0 (default)
Language
ENG (English)
Type
Calculative / Quantity
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