No, you should not put water on an electric stove burner to extinguish it. Electric stove burners are not meant to be extinguished with water, and doing so can be extremely dangerous.
Electric stove burners work by heating up an electric coil or element, and they don't produce an open flame like gas burners. If you pour water on a hot electric burner, the water can instantly turn into steam, which can cause the hot oil or grease on the burner to splatter or even explode, leading to severe burns or injuries.
If you need to extinguish an electric stove burner, simply turn off the stove using the appropriate control knob or switch. Never attempt to put water or any other liquid on an electric stove burner while it is still hot or operating. Always prioritize safety and follow the manufacturer's instructions for operating and maintaining your electric stove.