magento 2 how to get parent category id current category

$objectManager = \Magento\Framework\App\ObjectManager::getInstance();
   $category = $objectManager->get('Magento\Framework\Registry')->registry('current_category');//get current category
  $current_cat = $category->getId(); // current category id

  $parent_cat =  $category->getParentCategory()->getId(); // parent category id