Passing Cat ID

Everyone, I am a newb at this, so please bare with me. I have limited knowledge when it comes to php, but I’m learning.

The problem I am having is this. I have multiple categories, and some have sub-cats. What I would like to have happen is that when you go to a category page, that categories sub-cats are displayed on the sidebar.

I am using Daiko’s text widget, with widget logic plugin to control what pages each widget is displayed on. The coding I am using is as follows.

<?php

wp_list_cats ("optioncount=$c&hierarchical=$h&sort_column=s&child_of=31");

This works for the category 31, but what I need to do is pass the current category page id, to a variable, and use that variable in place of “31”.

after searching I’ve found this snipet “get_query_var(‘cat’)”. Which should return the current category, but I am unsure how to use it, and what the syntax should be.

Thanks in advance for your help.