Kinjalgp, that's wrong. The units of the product of R and C is seconds. If RC=1, then that is a one second time constant. Petersmith says he wants to deliver energy for one time constant, not one second. Suppose R=1 kohm and C=1 uF. Then RC (one time constant)=1 millisecond. Does RC=1 in this case?
If we want to deliver energy for one time constant, then in the equation you posted, which I agree is correct, t=RC, or, as I said, t/RC=1.
I do want to clarify the meaning of VF. In this case, I have assumed that we are discharging the cap through a resistor whose other end is connected to ground (while the switch is closed). In this case then, VF=0, and the equation simplifies to the equation I posted:
Vc=VI*e^(-t/RC)
Ron