For Prob. $4\mathrm{.}66.$

$4\mathrm{.}67$ The variable resistor $R$ in Fig. $4\mathrm{.}133$ is adjusted until it absorbs the maximum power from the circuit.

$($a$)$ Calculate the value of $R$ for maximum power.

$($b$)$ Determine the maximum power absorbed by $R.$

Figure $4\mathrm{.}133$

For Prob. $4\mathrm{.}67.$