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In this paper, we investigate the capacity of CSMA (carrier sense multiple access) based wireless multi-hop networks with random topologies described by the hop length distribution. First we develop an analytical model for the effective link capacity as a function of transmit power adaptation policy, physical carrier sense threshold, hop length distribution and medium access probability of p-persistent CSMA. Secondly, we devise an optimal transmit power control scheme that maximizes the network capacity by adjusting the transmit power and the corresponding physical carrier sense threshold. Thereafter, it is extended for the joint optimization of these parameters with the medium access probability of CSMA. Finally we compare the optimal power control scheme with the minimum transmit power policy in. Results show that the proposed power control scheme optimally trades off the spatial reuse (number of interfering links) to the link SIR (signal-to-interference ratio) and achieves an amount of ~%15 increase in network capacity when both schemes employ joint optimization.