Question

explain the time- constant of R-C circuit and write its dimensions

Answer 1

The quantity τ = RC is time constant of CR circuit.
This equation governs charging of capacitor through resistor R.
We may define time constant of CR circuit as the time in which charge on the capacitor grows to 63.2 % of the maximum value of charge.
If RC is large, both the charging and discharging of the capacitor in CR circuit are slow and vice - versa.

Answer 2

The RC time constant, also called tau, the time constant (in seconds) of an RC circuit, is equal to the product of the circuit resistance (in ohms) and the circuit capacitance (in farads), i.e.

{\displaystyle \tau =RC}

It is the time required to charge the capacitor, through the resistor, from an initial charge voltage of zero to ≈63.2 percent of the value of an applied DC voltage, or to discharge the capacitor through the same resistor to ≈36.8 percent of its initial charge voltage. This value is derived from the mathematical constant e, specifically {\displaystyle 1-e^{-1}}, relating to the voltage across the capacitor versus time:

Charging toward applied voltage {\displaystyle V_{0}:\quad V(t)=V_{0}(1-e^{-t/\tau })}[1]Discharging toward zero from initial voltage {\displaystyle V_{0}:\quad V(t)=V_{0}(e^{-t/\tau })}