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Nothing noticeable. DC power is not transmitted between the coils of a transformer. There would be no current on the other side of the transformer, unless the power of the source was constantly modulated. bescause flux does not change its state.

after some time excessive heat is produced and winding may burn

Answer

A transformer's primary winding presents two forms of opposition to current flow. The first is resistance, which is dependent upon the length, cross-sectional area, and resistivity of the wound conductor. The second is reactance, which depends upon the inductance of the winding and the frequency of the supply. Resistance opposes both AC and DC currents, while reactance opposes only AC current. In the case of a transformer's windings, the resistance is relatively low while the reactance is very high. When an AC voltage is applied, the reactance is sufficiently high to limit the value of AC current flowing through the winding. However, the resistance is so low that a large current would flow if an equivalent DC voltage was applied instead. This current would likely overheat the winding's insulation, resulting in its breakdown, causing a short circuit(s) which could severely damage the transformer.

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