RC Circuit ; why RC=(VT/2 delta V)

[tom25]

Homework Statement

I need to prove that RC=(VT/2 delta V)


Select the circle components of Charging and discharging of a capacitor
Measure the resistance of resistor with a multimeter
When you run a different frequency the cycle time change
run different frequency that T<<tao, T=tao, T>>tao
Choose components So that T<<tao,
V - the voltage of Function Generator
delta V= Voltage amplitude

Homework Equations

when -T/2<t<0
Q(a)=-cv+Ae^(-t/tao)

when T/2>t>0
Q(b)=cv+Be^(-t/tao)

A=(2cv)/(e^(T/2tao)+1)
B=(-2cv)/(e^(-T/2tao)+1)

The Attempt at a Solution

Q=VC

Va=Qa/C

Vb=Qb/C

delta V= Vb-Va

RC=tao

I place Vb-Va on RC=(VT/2 delta V) and I played with the equation

but I didn't get RC=(VT/2 delta V)

 

[tom25]

I tried another solution but I got stuck:

Va=Qa/C

I used Va:

delta V= V(0)-V(-T/2)

VT/2 delta V

e^(T/2tao)=1+T/2tao -- taylor

and I get RC+T/4

what wrong?