Fixed radius models are good representatives of distributed wireless sensor networks. Here nodes are uniformly randomly distributed in the sensing region and are assumed to have a fixed transmission radius r. It has been shown that in this model phase transition like behavior with respect to r, exists for various properties such as connectivity, presence of cliques, Hamiltonian paths and Hamiltonian cycles. In this paper we particularly concentrate on the phase transition behaviors for the appearance of a giant component in the networks and obtain an expression for the critical radius rc. We show that rc is inversely proportional to N, where N is the number of nodes in the network. We also further show that this threshold in terms of the average degree< k> of the network is about 5 and is independent of N. Using these results we propose two distributed algorithms that can be used as self-organizing rules to obtain a connected sensor network.