You have to use jQuery, especially if you use multiple forms. Than you can fire this code if you show the form.
try{
grecaptcha.reset()
}
catch(e){
null
}
grecaptcha.render('RecaptchaID', {
'sitekey' : 'YOUR_sitekey'
});
Everytime this script is fired, recaptcha will be reseted and a new one will be shown.
This is the Div for Recaptcha:
<div id="RecaptchaID"></div>
And place this at the End before </body>.