One time constant for a series RC circuit is also defined as the time in seconds required for the capacitor to charge to 63.2 percent of its final value. Show that this statement is true.
Write the capacitance voltage equation v_{C} when the capacitor is being charged.
v_C=V\left(1-e^{-t / R C}\right) (19-17)
One time constant T = RC. Substitute RC for t.
v_C=V\left(1-e^{-R C / R C}\right)=V\left(1-e^{-1}\right)=V(1-0.368)=0.632\ VSo v_{C} is 63.2 percent of V in one time constant.