In the circuit shown, the silicon BJT has $\beta = 50$. Assume $V_{BE}= 0.7 \: V$ and $V_{CE(sat)}= 0.2 \: V$. Which one of the following statements is correct?
- For $R_{C}= 1$ $k$$\Omega$, the BJT operates in the saturation region
- For $R_{C}= 3$ $k$$\Omega$, the BJT operates in the saturation region
- For $R_{C}= 20$ $k$$\Omega$, the BJT operates in the cut-off region
- For $R_{C}= 20$ $k$$\Omega$, the BJT operates in the linear region