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Half-Life for Capacitors in Parallel and in Series

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Physics Electricity Direct Current

https://texercises.com/exercise/half-life-for-capacitors-in-parallel-and-in-series/

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Exercise:
The half-lives for discharging two different capacitors through the same resistor are TaO and TbO respectively. Calculate the half-life when the two capacitors are connected in parallel or in series.

Solution:
The time constants for the capacitors with capacitance C_ and C_ are given by tau_ R C_ tau_ R C_ The total capacitance for the two resistors in parallel is C_p C_+C_ and therefore the time constant is tau_p R C_p R C_+C_ R C_ + R C_ tau_+tau_ Multiplying both sides by ln we find the relation for the half-lives: T_p TpF Ta+Tb resultTpP In the same way the relation for the half-life with the two capacitors follows from the rule for the series capacitance: T_s TsF leftfracTa+fracTbright^- resultTsP

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Attributes & Decorations

Branches	Direct Current
Tags	capacitor, half-life, parallel, rc circuit, serie
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Difficulty	(2, default)
Points	0 (default)
Language	(English)
Type	Calculative / Quantity
Creator	by
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