current transformer behaving like voltage transformer
The differences between a voltage transformer and a current transformer are only in the construction. The theory is the same for both.

The secondary current in a (current) transformer is not constant, regardless of load. The secondary current is only proportional to the primary current with the secondary short-circuited. With the secondary open-circuit, the secondary voltage is proportional to the rate-of-change of the primary current, and might be very large if the primary current changes rapidly.

With a resistive load, the output voltage will depend on both the primary current and it's rate-of-change. Manufacturers of current transformers therefore quote a maximum load resistance (or a maximum secondary voltage) for which the transformer's primary/secondary current ratio will remain in specification.

Here is a Bode plot (on logarithmic axes) of an ideal current transformer. As you would expect, at dc there is no output. Ls represents the secondary inductance, and RL is the resistance in the secondary circuit, ie the sum of the secondary resistance and the load resistance.



If we start with the black line as our transfer function, and our operating frequency is indicated by the blue line, we get the expected 1/N current ratio. If we increase the load resistance RL enough (the red line), our blue line now intersects the transfer function at a lower current ratio. So we require \$R_L&lt;2\pi fL_S\$ for normal operation.