$1.(20$ points$)$ Linear DC$/$DC converters. A linear DC $/$ DC converter consists of a voltage source, a transistor, and a load in series. The voltage source is a battery that provides input power at $12\mathrm{.}0$ Volts DC$.$ Its load is a small audio system that operates at $5\mathrm{.}0$ Volts DC and draws $500$mA DC$.$ Answers the two questions while explaining the procedure.

a$.(10$ points$)$ The voltage across the transistor is

b$.(10$ points$)$ The energy efficiency of this linear power converter is