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9.A 5 μF capacitor is connected in series with a 2 MS2 resistor. A switch is thrown which connects 100 volts to the series combo. i. (5 pts) What is the time constant? i. (5 pts) How much energy will the capacitor have at full charge? iii. (5 pts) What is the capacitor voltage after 5 seconds? iii (5 pts) What is the capacitor voltage after 1 minute?
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Theng;ven data Capacitance (C) ะ 5AAf Resis tance () 2M2 Voltage o source (V 100 V The circuit da gran tor Scis RC circui is a follous Let Ve (f) 江 the instantiation voltage a cros the capa citos Apply kvL 01 the abo ve circuit , V,(t) Ri(t) +vc(t) d t d td t d Vc R c Inte grate on both the side cJdt -log (Vs -Vc L c Vs Vc Finding k At time to Ve o Substitute in ea 0, -t R C lo9sVe RC Er pressing in exponential , wegeFrom ,equation ③ we observe that R he time cons tant at uohich Ve ;s: 63.27. ot おna l value. 1) Time constantR てこ16 sec Time contant)..て-70sec )we know the formu la do the energy of the capacitor 31 2 Cafa citor i u orged at stead state on There tore,at t 。 2.2 2 5x10 2 .: Entrgy the capacitor have at gull tharge,o.o2TJ ii) capac; tot Vot fage at t=ssee. From equation ③, we have - 50 100 CI-e ve = 39.347 v capacitor vortage at tsseu 39.347 Voits. v) capacitor voltage at tebo sec; Again drom tquation Q , i At t=60 , Ve Ma) -6 :Capactor voltage at t60 cees

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