r(e) Model of a Transistor
The transistor is simplified, and we get \$R_e I_e \$, with dependent source at collector as Ic=βIb. Now, these two are separated as the the voltage drop across \$R_e \$ is \$R_e I_e \$ and \$ I_e=I_c+I_b =&gt; \beta I_b+I_b =&gt; (\beta+1)I_b\$ .
put value of \$I_e \$ in \$R_e I_e \$, the drop becomes \$(β+1)R_e I_e \$. Now, \$(β+1)R_e\$ is your resistance and \$ I_b \$ is current flowing through it and hence both are separated. Also, as (β+1)≈β the resistor leg is \$ \beta R_e\$ .