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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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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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Direct Current
Tags
capacitor, half-life, parallel, rc circuit, series
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Difficulty
(2, default)
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Language
ENG (English)
Type
Calculative / Quantity
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