The phenomenon of electromagnetic induction refers to the generation of an electric current in a coil when there is a change in the magnetic field through the coil. It is important to understand each option to determine the correct answer.

Option 1: The production of induced resistance in a coil when the magnetic field changes with time is not correct. Resistance is a property that opposes the flow of current, and it is not directly related to the changes in the magnetic field.

Option 2: The generation of an electric current in a coil when an electric field changes with time is also incorrect. The phenomenon of electromagnetic induction specifically involves the interaction between a changing magnetic field and a coil.

Option 4: The production of voltage in a coil when an electric field changes with time is not accurate. Voltage is typically associated with the potential difference between two points and is independent of the electric field changes.

The correct answer is option 3, which states that the phenomenon of electromagnetic induction involves the production of an electric current in a coil when the magnetic field changes with time. This concept is the basis for various applications, such as generators and transformers, which rely on the conversion of mechanical energy into electrical energy.