A small thermoelectric generator $($single pair$)$ is equipped with two thennal sensors$,$ one

measuring TH$=1000$K and one measuring Tc$=500$K$.$ An electric heater warms up the

hotter side and all the heat thus generated is delivered to the device. When current I$=$O$,$ it takes $10$ W of electric power to operate the heater to maintain TH$=$lOOO K$,$ and the device develops $0\mathrm{.}5$ Vat its open$-$circuit condition.a$)$ What is the value ofl when it takes J$8\mathrm{.}3$ W to maintain Tir$-=1000$ K$?($b$)$ What voltages are necessary to drive the above current?Note: PH$=$k$($TH$-$Tc$)-$STHI$-0\mathrm{.}5$RI $2,$ P: Power, k: thermal conductivity, R: electrical resistance, S: Seebeck coefficient