Where do you find the part of th generator in cerulean gym on Pokemon heartgold?

You don't find the part of the generator in the Cerulean Gym in Pokemon HeartGold. The generator is already in place, and you need to activate it to defeat the gym leader, Misty.

Here's how you do it:

1. Enter the gym and proceed through the maze of water-type Pokemon trainers.

2. Reach the back room where the generator is located.

3. Interact with the generator. A Pokemon will be guarding it.

4. Defeat the Pokemon. This will activate the generator.

5. Battle Misty and defeat her to win the Cascade Badge.

The generator itself isn't a separate item you find. It's a fixed element within the gym that you need to activate to progress.