Q.The DC emitter current of the transistor is 3mA. Calculate the AC resistance of the emitter diode of silicon transistor.

In a working amplifier the DC bias current and the AC signal current flow through the same components at once, so the circuit is analysed in two independent parts.

DC equivalent circuit — reduce every AC source to zero and open-circuit every capacitor (a capacitor blocks DC). What remains is the bias network. The supply divides across $R_1, R_2$, giving $V_2 = V_{CC}\,R_2/(R_1+R_2)$; the base-emitter loop then gives the emitter current $I_E = (V_2 - V_{BE})/R_E$, and the collector loop gives $V_{CC} = V_{CE} + I_E R_E + I_C R_C$. This fixes the operating point. …