Capacitance vs. Resistance Proof

[checkmatechamp]

Can somebody confirm if this is correct? I'm trying to use a wye-delta transformation on capacitors to solve for equivalent capacitance, but to be super-precise, I want to put capacitance in terms of resistance.

I = C*(dV/dt)
V = IR, so I = V/R

V/R = C*(dV/dt)

(V*dt) = R*C* dV

Integrate both sides.

V*t = R*C*V

t = R*C which means that R = t/C

That makes sense, since people talk about a time constant, but I just want to be sure.

 

[Simon Bridge]

You need to specify the circuit ...

Note:
Your integration assumes that V is a constant with time, but your first equation assumes that dV/dt is not zero, therefore V does vary with time. This is a contradiction (unless I=0). Try using lower case for variable voltages and currents.