Now we have a computer at home (is connected to) the Internet.这句话是不是不太对啊

Now we have a computer at home (that/which is connected to) the Internet
不然定语从句缺少主语,成分残缺.恩恩 或者就是括号里面直接是connected to对吗对那就是过去分词作定语了，一样的。