For a voltage transformer: -
If the applied voltage were very low in frequency i.e. 0.1 Hz, the primary current taken (if the voltage were 120VAC or 230VAC) would be several tens of amps and the winding would fry and burn. Nonetheless, what about trying it at 1VAC? Now the current (remember we're talking 0.1 Hz) is a couple of hundred milliamps (that's OK) and the flux is just about avoiding saturation (phew) but, a decent flux rate of change is needed to produce the requisite voltage in the secondary and at 0.1 Hz it aint changing that quick so you get a really small output. No big deal output voltage and input voltage are still approximately related by the turns ratio but you can't connect to live and neutral anymore because it'll burn.
At some point above (maybe) 35 Hz, you can run full voltage.
Primary current is always defined by the "external circuit" - that's good because now we don't need to worry about saturation or the current getting bigger at lower frequencies. Normally the current transformer has a burden resistor of 1 to 100 ohms and this totally swamps the magnetization impedance; consider, at 50 Hz the mag inductance is 10 uH - this has a reactance of 3.14 milliohms. Now the burden may be 10 ohms and the winding ratio maybe 1:200 - referred to the primary the 10 ohms is 40,000 times smaller at 250 micro ohms. The mag inductive reactance (3 milliohms) is swamped by the primary-referred burden of 250 micro ohms.
At 5 Hz the burden is still 250 micro ohms and the mag reactance is 300 micro ohms - see how things are changing - what this means is that the CT at low frequencies can no-longer sustain the maths that underlies it. At 0.5 Hz the output will be negligible because the primary referred burden resistance is totally swamped by the extremely small magnetization impedance.
Equivalent circuits of VT and CT
Comparing CT with VT, you can forget about the primary DC resistance, leakage inductance and core losses - all you have a fat wire going thru a hole and it generates magnetism hence Xm is still present. If the secondary leakage impedances are small compared to the burden, then you can usually forget these as well. What remains is the burden (redirected to be on the primary) in parallel with Xm and, the burden normally dominates i.e. it is the lowest impedance because of turns-ratio-squared.