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Displacement current is a concept which deals with the flow of charges when there is a time-varying electric field. It is important to note that the displacement current is not the flow of actual charges, but the variation in the electric field producing an effect equivalent to the flow of charges.

Displacement current is not an actual flow of charges but a changing electric field that affects the magnetic field around it. According to Maxwell's equations, a changing electric field gives rise to a magnetic field, and vice versa. So, when either the electric or magnetic field is changing, there will be a displacement current.

Now let's analyze each option with the help of the understanding we have gathered from steps 1 and 2: (A) Displacement current is continuous when the electric field is changing in the circuit. - This statement is true as displacement current is related to the change in electric field. (B) Displacement current is continuous when the magnetic field is changing in the circuit. - This statement is true as well since a changing magnetic field affects the electric field, which in turn affects the displacement current. (C) In both types of fields. - Since both options (A) and (B) are true individually, this statement is also true. (D) Through wires and resistance only. - This statement is not correct because displacement current doesn't only exist through wires and resistance; it also exists in the dielectric materials and capacitors.

Given the understanding that displacement current is constant when either the electric field or the magnetic field is changing, we can conclude that the correct answer is option (C): in both types of fields.