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So recently I was installing these old fairy lights and its plug was burnt due to faulty connections, So I bought a new plug and replaced the old plug. I was wondering why do these fairy lights do not have any polarity and why do the sockets in our household have no polarity?

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The "polarity" would distinguish between "hot" and "neutral". In India, "hot" is 230VAC or so relative to ground as well as neutral, whereas "neutral" is nominally at ground potential, so is typically much less dangerous if accidental contact occurs.

It would often be preferable to have a polarized plug because many devices such as "wall warts" that are just about as safe with mains connected one way or the other have a much larger potential with respect to ground when the mains is connected one way vs. the other. That is because there is a capacitor across the switchmode power supply transformer to reduce EMI on the output wires. If the capacitor fails (short, as capacitors are wont to do) you're likely to get a shock if it's connected the "wrong" way, but the "Y" capacitors are made to be very, very reliable.

Another motive is to reduce the risk with things like lamps where it's easy to contact the outer portion of the socket with your fingers when changing a bulb (thus potentially forming a path to ground through your body), but much more difficult to contact the center contact.

If there is a 3-wire socket provided, the plug should have a ground as well as being polarized (assuming it's wired correctly). Below is a photo of an Indian 3-wire plug from this video, with the popularization indicated in the molding.

enter image description here

Occasionally one sees polarized plugs with a plastic ground pin that serves only to enforce polarization (or perhaps to open the shutter on some outlets), but I'm not sure that's an officially sanctioned approach in India (or anywhere else).

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    \$\begingroup\$ I have no idea about india, but BS1363 explicitly endorses the concept of an "insulated shutter opening device" for non-rewirable plugs attatched to class 2 devices/cords. \$\endgroup\$ Oct 28, 2019 at 17:31
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If these lamps are incandescent bulbs then they don't care which way current is flowing to heat up and give light. Mains sockets have alternaring current so depending on country there is a sine wave of 50 or 60 Hz. Also depending on country, you may have polarised or unpolarised plug. It does not affect the current, it just specifies which terminal is the neutral wire (0V in respect to earth/groung) and which terminal is the live wire (AC sine wave in respect to neutral wire)

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  • \$\begingroup\$ I live in India , so , we have unpolarized plugs here , I am wondering how that works , since most devices like a charger used for charging a phone battery should have a polarity? \$\endgroup\$ Oct 28, 2019 at 10:19
  • \$\begingroup\$ At some point inside a charger or power supply the AC mains is rectified to DC. \$\endgroup\$
    – Justme
    Oct 28, 2019 at 11:09

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