Load PartialView with using jquery Ajax?

You could subscribe to the .change() event of the dropdown and then trigger an AJAX request:

<script type="text/javascript">
    $(function() {
        $('#meters').change(function() {
            var meterId = $(this).val();
            if (meterId && meterId != '') {
                $.ajax({
                    url: '@Url.Action("MeterInfoPartial")',
                    type: 'GET',
                    cache: false,
                    data: { meter_id: meterId }
                }).done(function(result) {
                        $('#container').html(result);
                });
            }
        });
    });
</script>

and then you would wrap the partial with a div given an id:

<div id="container">
    @Html.Partial("MeterInfoPartial")
</div>

Also why are you parsing in your controller action, leave this to the model binder:

[HttpGet]
public ActionResult MeterInfoPartial(int meter_id)
{
    var meter = entity.TblMeters.FirstOrDefault(x => x.sno == meter_id);
    return PartialView(meter);
}

Be careful with FirstOrDefault because if it doesn’t find a matching record in your database given the meter_id it will return null and your partial will crash when you attempt to access the model.