Equation 15 clearly states that the sensitivity to extended sources depends on the dilution of the synthesized beam in the primary beam. This is why this formulation of the sensitivity is well adapted to resolved sources.
For a given interferometer, the primary beamwidth is a fixed quantity while
the synthesized beam is to first order proportional to the longest baseline
in the current interferometer configuration. Hence, doubling the largest
baseline will multiply
by a factor
for the same
integration time or it will multiply the integration time by a factor
in order to reach the same sensitivity. This just reflects that
while the interferometer tries to mimic a single-dish antenna of same
diameter as the largest baseline, all the antenna of the interferometer
only fill a fraction of the total collecting area of the single-dish, this
fractions decreasing with a power of two as the baseline linearly
increases.