Cin in a bjt

hi everyone,
please clarify my doubt,
in a common emitter bjt, we have a Cin capacitor, between the base and the source.the source is 10V dc + 50mV ac. we say that since the base is at a positive voltage, the base-emitter junction in in forward biased mode.but since we have a capacitor, the entire dc voltage drop is across the capacitor so the voltage across the base - emitter junction is only 50mV. but the voltage needed to turn on the diode is atleast 0.7V.

You are correct in observing that the transistor won't work with only a capacitor in series with the base. The transistor needs a bias circuit after the capacitor to turn on the base-emitter junction and generate a collector-emitter bias current for AC amplification.