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You may not even need the series resistor but none of the Arduino pins themselves will supply enough current so you need some kind of switch controlled by the Arduino.

The polarity switching can be done with a single relay if you use a DPCO type.  They are essentially two mechanically linked but independent change-over switches. If you feed + and - to the moving (common) contacts and link the normally open switch on one pole to the normally closed switch on the other, the polarity will reverse when you energize the relay coil.

Brian.