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A capacitor `C` is in series with a resistor `R` . The capacitor is charged, and then a switch is closed to complete the circuit. At what time has...


After the switch is closed, the charge on the capacitor decreases as


`Q(t)=Q_0e^(-t/(RC))`


The initial energy of the capacitor is 


`U=Q_0^2/(2C)`


So we want to solve for a time such that


`Q(t)^2/(2C)=1/2 Q_0/(2C)`


`2= e^((-2t)/(RC))`


`t=(RC ln(2))/2`


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