A: If the transformer is connected to a power input of course it will draw current. The primary is a long wire it has own resistance wrap around an iron core. Of course there will be primary current whether there is a load on the secondary or not.
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A current transformer is used in high voltage circuits where it is not possible to measure current directly. A CT is a step up transformer with only one turn in primary. There will be as many cores based on the purposes like metering, protection etc. The secondary of a CT should never be kept open circuited bcoz very high flux will be developed in the secondary and hence it may be damaged.
Leakage reactance is useful for limiting the short circuit current in transformer and generators. therefore normally the reactance of transformer varies for 4.5% for distribution transformer to 12.5% for 400KV class.
Unit or say Rating of transformer is in KVA and not in KW because copper loss of a transformer depends on current and iron loss on voltage. Hence, Total transformer loss depends on volt-ampere ( VA ) and not on phase angle between voltage and current i.e. it is independent of load power factor. That is why Unit or say Rating Of Transformer Is In KVA and not in KW.
If the frequency is kept the same, you will overexcite the transformer, and it will draw excessive current (similar to inrush currents). Insulation tests are performed on transformers above nominal voltage, but they are performed at higher than rated frequency to keep the volts per hertz roughly equal to prevent overexciting the core.
If you are referring to a pole-mounted distribution transformer, it's in order to maintain a safe clearance between its high-voltage connections and ground level.