The average power absorbed by the 10 resistor is kW vs 32Z 4

The average power absorbed by the 10- resistor is (__________)kW.?

Solution

from the circuit

IO=(32<45-0.1VO)/4

4IO=32<45-0.1VO

0.1VO+4IO=32<45 ------------------(1)

FROM THE CURRENT DIVISION FORRMULA

current through 10 ohms resistor=(8IO*5i)/(5i-5i+10)=(j5*8IO)/10

VO=- current through 10 ohms resistor*10

VO=(-10*j5*8IO)/10=-j5*8IO ----------------------(2)

substitute IO=VO/(-j40) from equation (1).

0.1VO-(4VO/j40)=32<45

j4VO-4VO=32<45*j4

VO(j4-4)=j4*32<45

VO=22.627 volts.

power absorbed by 10 ohms resistor=VO^2/10=(22.627)^2/10=51.198 watts.