这三个短语都是被动结构：
1.be connected to :把...连上,例如,Please connect the computer to the Internet.
2.be connected with :把...与...连接起来.例如,It serves as a bridge which connects the mainland with the rest of the world.(它是连接祖国大陆与世界其它地方的桥梁）.The mainland is connected with the rest of the world.
3.be connected by：被...连接在一起.例如,The whole world is connected with by computers and it is becoming smaller and smaller.(整个世界被电脑连在了一起,世界变得越来越小了）.
祝你一切顺利!