  Pulse delay with the group velocity dispersion (GVD) characteristics was
studied in the V-type electromagnetically induced transparency in the hyperfine
levels of $^{85}Rb$ atoms with a closed system configuration. The phase
coherency between the pump and the probe laser beams was maintained. We studied
the pulse delay and the group velocity dispersion characteristics with the
variation of the pump Rabi frequency taking temperature as a parameter. We
observed a maximum of $268$ $ns$ pulse delay for $21.24 MHz$ pump Rabi
frequency at $55^0C$ temperature of the Rb vapour cell. For a better
understanding of the experimental results, we have derived an analytical
solution for the delay characteristics considering the thermal averaging. The
analytical solution was derived for a three level V-type system. The
theoretical plots of the delay and the group velocity dispersion show the same
characteristics as we observed in the experiment. This analytical approach can
be further generalized for the higher level schemes to calculate different
quantities such as susceptibility, group velocity delay or group velocity
dispersion characteristics.
