Two lamps one rated `100 Omega` at 220 V and the other 60 W at 220 V are connected in parallel to a 220 volt supply. What current is drawn from the supply line?

Explanation

Data for
`{:("Lamp 1", "Lamp 2"),("Rated power" P_(1) = 100 W, "Rated power" P_(2) = 60 W),("voltage" V_(1) = 220 V, "Voltage" V_(2) = 220 V),("Resistance" R_(1) = (V_(1)^(2))/(P_(1)),"Resistance" R_(2) = (V_(2)^(2))/(P_(2))):}`
Since `R_(1)` and `R_(2)` are connected in parallel effective resistance,
`R_(P) = (R_(1) R_(2))/(R_(1) + R_(2)) = ((V_(1)^(2))/(P_(1)) (V_(2)^(2))/(P_(2)))/((V_(2)^(2))/(P_(1)) + (V_(2)^(2))/(P_(2)))`
`R_(P) = (V_(1)^(2) V_(2)^(2))/(P_(2) V_(1)^(2) + P_(1) V_(2)^(2)) = ((220)^(2) (220)^(2))/(60 xx (220)^(2) + 100 xx (220)^(2))`
`:. R_(P) = ((220)^(2))/(160) = (48400)/(160) = (4840)/(16)`
Current is drawn from supply line,
`i = ("Main line voltage"(V))/("Resistance" (R_(P)) "connected")`
`implies i = (220)/(4840) xx 16 = 0.727 A`
`:. i = 0.73 A`