Explanation:
When an inductor is at t=0 with zero initial conditions, it acts as an open circuit. This is because at t=0, the current through the inductor is zero and there is no voltage drop across it. As a result, the inductor appears as an open circuit to the circuit.

Here is a detailed explanation:

What is an inductor?
An inductor is a passive electronic component that stores energy in a magnetic field when electric current flows through it. It consists of a coil of wire that generates a magnetic field when current flows through it.

What are initial conditions?
Initial conditions refer to the state of a circuit or system at a particular point in time. In the case of an inductor, the initial conditions refer to the current and voltage across it at a particular point in time.

Why does an inductor act as an open circuit at t=0 with zero initial conditions?
When an inductor is at t=0 with zero initial conditions, the current through the inductor is zero. As a result, there is no voltage drop across the inductor. Therefore, the inductor appears as an open circuit to the circuit.

What happens when an inductor is connected to a voltage source?
When an inductor is connected to a voltage source, it initially acts as an open circuit due to its zero initial conditions. However, as the voltage source applies a voltage across the inductor, the inductor starts to build up a magnetic field. This causes the inductor to resist the flow of current, resulting in a gradual increase in the current. Eventually, the current through the inductor reaches a steady-state value, where the inductor acts as a short circuit.

Conclusion:
In summary, an inductor at t=0 with zero initial conditions acts as an open circuit because there is no current flowing through the inductor, and hence no voltage drop across it. As a result, the inductor appears as an open circuit to the circuit.