The CR battery is a coin type battery that has multiple uses. Usually, such batteries are best for low power devices. CR is a term used by almost every manufacturer. The CR batteries last for several months, if not years.
It entirely depends on the electrician that where does he/she want to use it. You can find different CR batteries in the market, and each one may have a different maker.
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The DL battery is actually a CR battery, but manufactured by Duracell. Since there is no difference between the dimension and thickness of a DL and CR battery, both can be used for the same purpose.
Duracell uses this unique generic designation just to make the products different from what is commonly available in the markets. Since Duracell makes battery with higher capacity, its administration utilises every possible option to spread the reputation. And the trick of changing the generic designation to a unique one has worked really well.
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