WordPress: Add 'img-responsive' class via filter to 'the_content'

functions.php

// add default class for img-responsive
function add_image_responsive_class($content) {
   global $post;
   $pattern ="/<img(.*?)class=\"(.*?)\"(.*?)>/i";
   $replacement = '<img$1class="$2 img-responsive"$3>';
   $content = preg_replace($pattern, $replacement, $content);
   return $content;
}
add_filter('the_content', 'add_image_responsive_class');

don't need the global $post