$*5\mathrm{.}69.$ Figure $5\mathrm{.}156$ depicts a "Darlington pair," where $Q_1$ plays a role somewhat similar to an emitter follower driving $Q_2.$ Assume $V_A=$ and the collectors of $Q_1$ and $Q_2$ are tied to $V_{CC}.$ Note that $I_{E1}($~~$I_{C1})=I_{B2}=\frac{I_{C2}}{}.$

$($a$)$ If the emitter of $Q_2$ is grounded, determine the impedance seen at the base of $Q_1.$

$($b$)$ If the base of $Q_1$ is grounded, calculate the impedance seen at the emitter of $Q_2.$

$($c$)$ Compute the current gain of the pair, defined as $\frac{I_{C1}+I_{C2}}{I_{B1}}.$