In this paper it is shown that the expected largest current in a random resistor network can be scaled as (InL)α , where L is the size of the network and the exponent a not only depends on dimension and the ratio of two conductances in the network, but also depends on the value of vertex angle β of the defects remarkably. This result follows from an analysis of the funnel configuration with a channel in it. Here we have also suggested a qualitative explanation concerning the difference in the values of exponent α when σ2→0 of Machta et al. and DEL theory.