The circular product is not having the same plasmids as before but the plasmids have same restriction sites that's why they able to ligate.
Plasmids are small, circular, extra-chromosomal DNA molecules found in a wide range of microorganisms, most notably bacteria, that can replicate independently of their hosts.
Whether or not the bacterial host is replicating its own DNA, plasmids can be copied numerous times, and each time a plasmid vector is copied, the introduced DNA it contains is as well. They are rounded. Circular DNA is ideal for incorporating additional DNA sequences.
Although occasionally linear or RNA-based plasmids exist, plasmids are typically circular DNA molecules. They can be single or multiple copies, and they can contain anywhere between a few dozen and several hundred genes.
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