Can a connected coaxial cable give you an electric shock?

How much current is in a TV coaxial cable. if I cut the cable and stick it on my tongue, will it shock me?

I strongly recommend you do not do that, while the voltage and current should be very small, and should not shock you (though you might feel it on your tongue, I'm not sure about that) there is alway a chance something is connected wrong some where, especially don't try this during a lightning storm.
The voltage is less than 1 volt, it will not hurt you.
If the cable is connected to a television signal, the voltage should be low enough to be harmless. But it's never a good idea to be careless with electricity of any sort.

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