Very recently google changed the url of recaptcha plugins javascript. That is why recaptcha is not working in joomla websites anymore.
Old recaptcha javascript url was http://api.recaptcha.net/js/recaptcha_ajax.js
Now that link gives an 404 error. New url is http://www.google.com/recaptcha/api/js/recaptcha_ajax.js
All you have to do is edit this file in your joomla website
\plugins\captcha\recaptcha\recaptcha.php
Go to link 22 where you will find this
Replace this code with the code below
and save the file, Recaptcha will start working again.. I hope an update in joomla will fix this.
Old recaptcha javascript url was http://api.recaptcha.net/js/recaptcha_ajax.js
Now that link gives an 404 error. New url is http://www.google.com/recaptcha/api/js/recaptcha_ajax.js
All you have to do is edit this file in your joomla website
\plugins\captcha\recaptcha\recaptcha.php
Go to link 22 where you will find this
const RECAPTCHA_API_SERVER = "http://api.recaptcha.net";
Replace this code with the code below
const RECAPTCHA_API_SERVER = "http://www.google.com/recaptcha/api";
and save the file, Recaptcha will start working again.. I hope an update in joomla will fix this.