I've been studying NPN's and I'm trying to calculate the voltages and currents.
Consider the following transistor circuit
simulate this circuit – Schematic created using CircuitLab
with Vb, Vc and Ve the voltage at Q1's base, collecter and emitter respectively. Assume the sources and resistors are chosen in a way that Q1 is operating in forward active region, so $$V_C > V_B > V_E$$ In active region the following relation applies $$I_C = \beta I_B$$ and $$I_E = I_B + I_C$$ With network analysis we can then find $$I_C = \frac{V_{EQ}-V_{BE}}{\frac{R_B}{\beta} + R_E\frac{\beta +1}{\beta }}$$ From this point I'm not sure how to proceed; When looking up Beta (or Hfe) in the 2N2222 datasheet
or by graph from this datasheet
we see that Hfe depends on the both Ic and Vce, but in order to calculate Ic we need to know Hfe. So how do I get an exact answer for Ic (and thereby solving Ib, Ie, Vb, Vc and Ve)?