To properly connect a broken wire, follow these steps:

1. Identify the type of wire: Determine if the wire is solid-core or stranded. Solid-core wires are easier to work with but can be brittle, while stranded wires are more flexible but can be more challenging to connect.

2. Strip the wire ends: Use a wire stripper to remove about 1/2 inch of insulation from both ends of the wire. Be careful not to cut into the wire itself.

3. Clean the wire ends: Use a wire cleaner or sandpaper to remove any oxidation or dirt from the exposed wire ends. This ensures a good electrical connection.

4. Choose the appropriate connector: Select a connector that matches the wire size and type. Common connectors include spade connectors, crimp connectors, and screw terminals.

5. Crimp the connector: If using a crimp connector, insert the stripped wire into the connector and use a crimping tool to secure it. For spade connectors, simply push the wire into the connector and twist it until it's tight.

6. Insulate the connection: Cover the connector with heat shrink tubing or electrical tape to insulate the connection and prevent short circuits.

7. Test the connection: Use a multimeter to check the continuity of the wire connection. Ensure that the multimeter reads a low resistance value, indicating a good connection.

Properly connecting a broken wire is crucial for maintaining electrical integrity and safety. According to a study by the National Fire Protection Association (NFPA), electrical failures are a leading cause of home fires and injuries. Ensuring that wire connections are secure and insulated can significantly reduce the risk of electrical hazards. Additionally, a report by the U.S. Consumer Product Safety Commission (CPSC) states that faulty electrical connections are responsible for approximately 25% of all home fires. By following the steps outlined above, individuals can prevent potential accidents and maintain the functionality of their electrical systems.