Show subcategories of current category

Ok, I am having no luck finding a solution for this, so maybe you can help me solve it.

I am setting up a directorystyle FAQ database and I am tryiong to figure out how to display subcategories of the current category.

I can list the categories through <?php wp_list_categories('&title_li=&show_count=1&child_of=1'); ?>

But I would like to be able to dynamicly replace child_of=x so that the x is the number of the category currently visited. So if I am clicking through to category with the ID of say…47 the code should change to child_of=47 automaticly.

Any help would be much appreciated.