Q1: An 8 V power source is charging a capacitor. How many volts will be across the capacitor at the second time constant?

ANS:D - 7 volts

We know that voltage across capacitor at any instant..... Vc = Vdc ( 1 - e^(-t/RC)) At second time constant i.e., 2t Vc = Vdc ( 1 - e^(-2t/t)) \\ RC = t Here Vdc = 8V Vc = 8V ( 1 - e^-2) Vc = 8V ( 1 - (1/e^2)) Vc = 8V ( 1 - (1/2.718^2)) \\ e = 2.718 exponential constant Vc = 8V ( 1 - (1/7.387)) Vc = 8V ((7.387 - 1) / 7.387) Vc = 8V ( 6.387 / 7.387 ) Vc = 8V ( 0.8646) Vc = 6.9168 or apporx. 7V t = RC , e = 2.718 and Vdc = X @ different time constant instant voltage will be.... 1t:-X*(1 - e^(-1t/t))=X*(1 - e^-1)=X*(1 -(1/e^1)) = X*0.632 2t:-X*(1 - e^(-2t/t))=X*(1 - e^-2)=X*(1 -(1/e^2)) = X*0.865 3t:-X*(1 - e^(-3t/t))=X*(1 - e^-3)=X*(1 -(1/e^3)) = X*0.950 4t:-X*(1 - e^(-4t/t))=X*(1 - e^-4)=X*(1 -(1/e^4)) = X*0.982 5t:-X*(1 - e^(-5t/t))=X*(1 - e^-5)=X*(1 -(1/e^5)) = X*0.993