WordPress address URL and bloginfo

I have updated my WordPress Address (URL) and Site Address (URL) to be https:// in the General Settings of WordPress as I have added a secruity certificate to the hosting.

Should the css url automatically update to reflect the new address if I’m using

        <link rel="stylesheet" type="text/css" href="<?php bloginfo('stylesheet_url'); ?>" /> 

in the header code.

The url is now https:// but the css url is still pointint to http://

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