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https://texercises.com/exercise/charging-current/
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Exercise:
A capacitor is charged through a RO resistor on a voltage supply with VO. The half-life for the charging process is ThO. Calculate the current at the ning and tO after the start of the charging process.

Solution:
The initial current is given by the total voltage and the resistance: I_ IoF fracVR Io approx resultIoP- The current exponentially decreases with the same half-life. The current after the time tT_// is It I_ e^-t/tau fracDelta V_R e^-fracT_/ tau fracDelta V_R e^-fractau ln tau fracDelta V_R e^-fracln fracDelta V_R leftfracright^frac IF fracVsqrt timesR I approx resultIP-
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Exercise:
A capacitor is charged through a RO resistor on a voltage supply with VO. The half-life for the charging process is ThO. Calculate the current at the ning and tO after the start of the charging process.

Solution:
The initial current is given by the total voltage and the resistance: I_ IoF fracVR Io approx resultIoP- The current exponentially decreases with the same half-life. The current after the time tT_// is It I_ e^-t/tau fracDelta V_R e^-fracT_/ tau fracDelta V_R e^-fractau ln tau fracDelta V_R e^-fracln fracDelta V_R leftfracright^frac IF fracVsqrt timesR I approx resultIP-
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Branches
Direct Current
Tags
capacitor, charging, dc circuit
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Difficulty
(3, default)
Points
0 (default)
Language
ENG (English)
Type
Calculative / Quantity
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Link