Time constants of RL and RC circuits are respectively:

R = 1 Ω; L = 1 H and C = 1 F 

Concept:

We can use Kirchhoff’s Voltage Law, (KVL) to define the individual voltage drops that exist around the circuit and then hopefully use it to give us an expression for the flow of current.

\(I_t = \frac{V}{R}\left( {1 - {e^{\frac{{Rt}}{L}}}} \right)\)

The Time Constant, ( τ ) of the LR series circuit is given as L/R and in which V/R represents the final steady-state current value after five-time constant values.

RC Charging Circuit

When the capacitor is said to be fully charged, t = ∞, i = 0, q = Q = CV. At infinity, the charging current finally diminishes to zero and the capacitor acts like an open circuit with the supply voltage value entirely across the capacitor as Vc = Vs.

The time constant is given as τ = RC.

\({V_c} = {V_s}\left( {1 - {e^{\frac{t}{{RC}}}}} \right)\)

Calculation:

Given:

R = 1 Ω; L = 1 H and C = 1 F 

τ of LR circuit is 

\(τ=\frac{L}{R}=\frac{1}{1}\) = 1 sec.

τ = RC =1 × 1 = 1 sec.