How to change the cookie in each click?

Question

I am doing an exercise to change the cookie at each click through ajax. I would like to set each click a different cookie according to the content that was sent by ajax. I am sending this Ajax to exchange the cookie.

<script>
jQuery(function(){
    /////////////////////////////////////////
    $(".cidade").on("click", function(event){
        ///////////////////////
        event.preventDefault();
        cidade = $(this).attr("id");

        $.ajax({
            url: "cookie.php",
            data: {
                cidade: cidade
            }
        });
    });
});
</script>

I would like your help to build a simple PHP script to exchange the cookie and have it presented in the next refresh. I did that which I think is pretty ugly and didn’t work. He takes the first cookie but not the others.

<?php
    if( isset($_REQUEST['cidade']) ){
        ///////////
        ob_start();
        setcookie("cidade", "", time()-3600);
        $cidade = $_REQUEST['cidade'];
        setcookie("cidade", $cidade);
        echo $cidade;
        /////////////
    }
?>