From $$High surface area carbon from polyacrylonitrile for high$-$performance electrochemical capacitive energy storage$$ by Gupta answer the following

$($a$)$ The authors report a specific capacitance for the high surface area $(3550$ m$2/$g$)$ sample $$A$-$PAN$$ of $150$ F$/$g at $1$ A$/$g current density in the pure EMIMBF$4$ electrolyte $($see orange curves in Graphs $2$b$-$c$).$ What is the approximate time constant for charging the double layer for electrochemical capacitors made from A$-$PAN and using the EMIMBF$4$ electrolyte? Assume that a $50$ micron thick separator was used in the experiments, the mass of A$-$PAN is $1$ g$,$ and estimate the resistance of the electrolyte from the ohmic drop in Graph $2$b$.$

$($b$)$ The authors use electrochemical impedance spectroscopy $($EIS$)$ to compare the properties of the $$A$-$PAN$$ samples with the $$AC$$ sample. How do they determine that AC has higher electrical conductivity but lower ion diffusivity than $$A$-$PAN$?$ The Nyquist plots are the second set of graphs

Figure S$1.($a$)$ Nyquist plots of symmetric configuration supercapacitors for AC and A$-$PAN in different electrolytes: $1MEMIMB{F}_4$

in acetonitrile and pure $EMIMB{F}_4.($b$)$ Nyquist plots of commercial AC and A$-$PAN in Li half cells.