Question #209629

The time constant of an RC circuit is 0.6 s. a) To what voltage can the capacitor be charged in 1 s if the voltage source is 100 V? b) In what time will the capacitor be discharged from that value to its half?


1
Expert's answer
2021-06-23T09:31:16-0400

(a) The voltage:


VC=VS(1etτ)=VS(1e10.6)=0.81VS,V_C=V_S(1-e^{-\frac{t}{\tau}})=V_S(1-e^{-\frac{1}{0.6}})=0.81V_S,

or 81% of the source voltage.

(b) Apply the same equation:


VC=0.5VS=VS(1etτ), 0.5=1etτ, t=τln(10.5)=0.6ln0.5=0.42 s.V_C=0.5V_S=V_S(1-e^{-\frac{t}{\tau}}),\\\space\\ 0.5=1-e^{-\frac{t}{\tau}},\\\space\\ t=-\tau\ln(1-0.5)=-0.6\ln0.5=0.42\text{ s}.


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