For the circuit shown below:

a$)$ Find the power factor of the circuit? $[2$ Marks $]$

b$)$ If the total power of the circuit is $1200$ W what is the power absorbed by each resistor? $[4\mathrm{.}5$ Marks $]$

c$)$ To what value the $\backslash (6\backslash$Omega $\backslash )$ resistor must be changed to result in the overall power factor $0\mathrm{.}9$ lagging? $[3\mathrm{.}5$ Marks $]$