Answer to Question #84095 in Electric Circuits for Oliver Jones

Question #84095
An example Capacitor is 24v and 1500μF and has a time constant of 0.15 Seconds.
I need to determine (using a discharge equation) the total charge, in coulombs discharged in the first 5 time constants and then predict how long it would take to discharge to 0.03 coulombs.
1
Expert's answer
2019-01-09T09:49:05-0500

The discharge equation:

"V(t)=V_0e^{-t\/T},"

where

"T=RC"

is a time constant. The total charge in the first 5 time constants thus is:

"Q=C\\cdot V(5T)=C\\cdot V_0e^{-5}=""=1.5\\cdot10^{-3}\\cdot24\\cdot e^{-5}=2.43\\cdot10^{-4} \\textrm{ C}."

Now predict how long it would take to discharge our capacitor to 0.03 coulombs (when the voltage of course will be

"V=Q\/C=0.03\/(1.5\\cdot10^{-3})=20 \\textrm{ V}"

). Express

"t"

from the first formula:

"t=-RC\\cdot {\\textrm{ln}\\frac{V}{V_0}}=-0.15\\cdot {\\textrm{ln}\\frac{20}{24}}=0.027\\textrm{ s}"

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