All extensions of public utilities within the City limits shall become a part of the aggregate property of the public utility, shall be operated as such, and shall be subject to all the obligations and reserved rights contained in this Charter and in the original grant hereafter made. The right to use and maintain any extension shall terminate with the original grant and shall be terminable as provided in Section 10.04 of this Charter. In case of an extension of a public utility operated under a franchise hereafter granted such right shall be terminable at the same time and under the same conditions as the original grant.