Two lamps, one rated 100W at 220 V, and the other 60 W at 220 V are connected in parallel to electric mains supply. What current is drawn from the line if the supply voltage is 220V ?

Explanation

The resistance of 100 W lamp,
`R_1 = V^2/P_1 =(220^2)/(100) =(220xx220)/100 =4840/10 Omega = 484 Omega`
The resistance of 60 W lamp,
`R_2 = V^2/P_2 = (220^2)/60 = (220xx220)/60 = 4840/6 Omega= 806.7 Omega`
When, these lamps are connected in parallel, their equivalent resistance `R_p` is given by
`1/R_p =1/R_1 + 1/R_2 = (R_2 + R_1)/(R_1 R_2)`
`:. R_p =(R_1 R_2)/(R_1 +R_2)`
`=(484 xx 806.7)/(484 + 806.7) = (390442.8)/1290.7 = 302.6 Omega`
The current drawn from the line,
`I = V/R_p =220/302.6 = 0.7270 ~~ 0.73A`