You need to clean the RCA connector with a 400 or 600 sand paper first. Than coat the small wire and the RCA connector with solder before soldering them together.
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If the RCA is gold plated, no cleaning is necessary. It should be nickeled at least- same thing. It should only need cleaning if it's copper or some other oxidized metal. Use an alligator clip on the front of the post to hold the back of the RCA upright, insert the wire into the post, apply heat evenly by touching a clean, tinned soldering iron tip to both metals to be joined. Touch the solder to the junction of the metals and it should flow nicely between them. One of these makes thing much easier: (http://www.mcmelectronics.com/product/22-6475) Here's a nice little treatise on proper technic: (http://www.epemag.wimborne.co.uk/solderfaq.htm)