The variable resistor in the circuit is adjusted for maximum power transfer to $R_o.$

a$.$ Find the value of $R_o.$

b$.$ Find the maximum power that can be delivered to $R_o.$

c$.$ Find a resistor in the Appendix closest to the value in part $($a$).$ How much power is delivered to this resistor?

Appendix

Common Standard Component Values of Resistors $(5\%$ tolerance$)$ in Ohms

$\backslash$table$[[10,100,1\mathrm{.}0$ k$,10$ k$,100$ k$,1\mathrm{.}0$ M$],[,120,1\mathrm{.}2$ k$,12$ k$,120$ k$,],[15,150,1\mathrm{.}5$ k$,15$ k$,150$ k$,1\mathrm{.}5$ M$],[,180,1\mathrm{.}8$ k$,18$ k$,180$ k$,],[22,220,2\mathrm{.}2$ k$,22$ k$,220$ k$,2\mathrm{.}2$ M$],[,270,2\mathrm{.}7$ k$,27$ k$,270$ k$,],[33,330,3\mathrm{.}3$ k$,33$ k$,330$ k$,3\mathrm{.}3$ M$],[,390,3\mathrm{.}9$ k$,39$ k$,390$ k$,],[47,470,4\mathrm{.}7$ k$,47$ k$,470$ k$,4\mathrm{.}7$ M$],[,560,5\mathrm{.}6$ k$,56$ k$,560$ k$,],[68,680,6\mathrm{.}8$ k$,68$ k$,680$ k$,6\mathrm{.}8$ M$]]$