Question

What supports the notion that the product of resistance and capacitance is the time constant for an RC circuit?

Answer 1

RC Time Constant
The time constant is a time period determined by the circuits R and C values. It is measured in seconds and denoted with the variable (?) tau. Tau is very easy to find since ? = R×C. An RC circuit’s time constant is useful because it directly relates the values of R and C to the capacitor voltage
In order to control the rate at which voltage changes in the circuit, we must consider the values of the capacitor and resistor. In a circuit, the capacitor controls the voltage across its terminals depending upon how charged it is. The resistor limits the amount of current passing through the capacitor, which in turn affects the rate at which the capacitor charges. The equation describing this relationship is Vc = Vs( 1 – e-t/RC), where:

Vc is the voltage of the capacitor
Vs is the voltage of the source
t is the time in seconds
R is the resistance in Ohms (?)
C is the capacitance in Farads (F)

Trying to limit the how fast the voltage Vccan change by manipulating the previous equation can be difficult. Instead we can use the circuits’ time constant to accurately approximate the capacitor’s voltage.