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Short Answer: Dew point measurement is necessary to ensure the moisture content of the cellulose insulation is low enough to safely energize the transformer (after filling with oil). Maximum acceptable moisture content varies with unit size/age, but less than 1% moisture content is generally acceptable.

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Q: Why dew point measurement is necessary in nitrogen filled transformer?
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If you are going by the electron configuration of nitrogen then the unpaired electrons in the 2p shell would indicate that it is paramagnetic. However experiments show that it is diamagnetic. You must remember that nitrogen is a diatomic element and as such is found as N2. The molecular orbital theory explains how there are no unpaired electrons in the bonds between the two N atoms. The 1s and 2s molecular orbitals are completely filled and all of the bonding 2p orbitals are also filled. There are no electrons in the any of the 2p anti-bonding orbitals. Seeing a molecular orbital diagram for N2 will clarify what i mean.