The time constant of an inductive circuit is denoted by the symbol L/RC and is derived from the equation for the voltage across an inductor in response to a step change in current. The time constant represents the time it takes for the current in the inductor to reach approximately 63.2% of its final value.

Explanation:

1. Inductive Circuit:
An inductive circuit consists of an inductor, which is a passive electrical component that stores energy in the form of a magnetic field. When a voltage is applied across an inductor, it resists the change in current flowing through it. This is due to the back EMF (electromotive force) generated by the inductor.

2. Voltage across an Inductor:
The voltage across an inductor can be described by the equation:
V(t) = L di(t)/dt
where V(t) is the voltage across the inductor at time t, L is the inductance of the inductor, and di(t)/dt is the rate of change of current with respect to time.

3. Step Change in Current:
Consider a scenario where a step change in current occurs in the inductive circuit. Initially, the current is zero and then suddenly increases to a final value. This step change in current results in a voltage across the inductor.

4. Time Constant:
The time constant of the inductive circuit, denoted by L/RC, represents the time it takes for the current in the inductor to reach approximately 63.2% of its final value. It can be derived by rearranging the equation for the voltage across the inductor.

5. Derivation:
Let's consider the equation for the voltage across the inductor and integrate it over time:
∫V(t) dt = L ∫di(t)/dt dt
∫V(t) dt = L ∫di(t)
∫V(t) dt = L(i(t) - i(0))

6. Time Constant Equation:
The time constant equation can be derived by rearranging the above equation as follows:
L(i(t) - i(0)) = V(t) dt
i(t) - i(0) = (1/L) ∫V(t) dt

Taking the limits from t = 0 to t = ∞, we get:
i(∞) - i(0) = (1/L) ∫V(t) dt

At t = ∞, the current reaches its final value i(∞). At t = 0, the current is zero, i(0) = 0. Therefore, we have:
i(∞) = (1/L) ∫V(t) dt

The term (1/L) ∫V(t) dt is the time constant of the inductive circuit, denoted by L/RC.

In conclusion, the time constant of an inductive circuit is given by L/RC. It represents the time it takes for the current in the inductor to reach approximately 63.2% of its final value.