$(20$ pts$)$ Consider an NPN Bipolar Junction Transistor for the follwoing questions.

a$.$ Draw and label the common$-$emitter circuit, including the following:

i$.$ Base, Collector, and Emitter voltages

ii$.$ Base and Collector currents

iii. Base resistance $R_B$

iv$.$ Collector resistance $R_C$

v$.$ ground

vi$.V_{CE}$

vii. $V_{BE}$

b$.$ If we intend to use the circuit as a switch, which regions of the common emitter characteristics will we operate between.

c$.$ At what base voltage $V_B$ does the transistor switch ON$.$

d$.$ Describe the procedure for ensuring the base current $I_B$ is sufficient for saturation.

e$.$ Described a single application of the common$-$emitter switch, and draw the circuit diagram of your application.