Referring to fig. 2.33 and taking V0=100V, R=1 Mega Ohm, what value of C is need

Question

Referring to fig. 2.33 and taking V0=100V, R=1 Mega Ohm, what value of C is needed so that Vout is 70V at 10.0 seconds after the switch closes?

Sketch V out versus time for the circuit shown in Fig. 2.33 after the switch is closed. Assume the capacitor is initially uncharged and that V0 = 12 V, R = 100 k ohm, and C = 10 mu F. Include appropriate numeric scales on the axes. figure 2.33 Circuit 2. 3. and 4. Referring to Fig. 2.33 and taking V0 = 100 V, R = I M ohm, what value of C is needed so that V out = 70 V at 10.0 s after the switch closes? Suppose we use the circuit of the previous problem and wait a long time after the switch is closed so that the capacitor is fully charged. Now we open the

Explanation / Answer

when the switch is closed capacitor gets charged following the equation

Vc=Vo(1-exp(-t/RC))

70=100(1-exp(-10/RC))

exp(-10/RC)=1-0.7=0.3

-10/RC=log(0.3)=-0.5228

C=(10^-5/0.5228)=19.12x10^-6=19.12uC

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