What is the time constant of an RC circuit resemble?

I have no idea what you mean. I'll just explain time constants.

Suppose we have an undriven RC circuit. V = IR and I = C (dV/dt), so the differential equation of the circuit can be written
dV/dt = - V/(RC)
The solution to this differential equation is
V(t) = V(0) e^(-t/(RC))
You'll notice that RC has units of time. Let's replace it with τ.
V(t) = V(0) e^(-t/τ)
τ is called the time constant of the circuit. It is a length of time that characterizes how long it takes the capacitor to discharge across the resistor. Let's try to get a good sense for it
e^-1 = 0.37
e^-2 = 0.14
e^-3 = 0.05
e^-4 = 0.02
That is to say, after one time constant has passed, 37% of the original voltage remains on the capacitor. After four time constants pass, less than 2% remains.
If you ever design circuits with capacitors, it's important to know about time constants and to calculate them ahead of time before prototyping the circuit. That way, you'll know that if you wait five time constants after disconnecting the power from your circuit, there's little chance you'll receive a shock.