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

Explanation

In order to solve this problem, first we have to calculate the resistances `R_(1)` and `R_(2)` of two lamps separately.
Now, Power, `P = (V^(2))/(R)`
For first lamp: `100 = ((220)^(2))/(R_(1))`
Resistance of first lamp, `R_(1) = ((220)^(2))/(100) = (220 xx 220)/(100) = (48400)/(100)`
`= 484 Omega` (1)
Again, Power, `P = (V^(2))/(R)`
For second lamp: `60 = ((220)^(2))/(R_(2))`
Resistance of second lamp, `R_(2) = ((220)^(2))/(60) = (220 xx 220)/(60) = (48400)/(60)`
`=806.7 Omega` ...(2)
The two lamps of resistance `484 Omega` and `806.7 Omega` are connected in parallel. So, the combined resistance of two lamps can be calculated as follows:
`(1)/(R) = (1)/(R_(1)) = (1)/(R_(2))`
`(1)/(R) = (1)/(484) +(1)/(806.7)`
`(1)/(R) = (806.7 +484)/(484 xx 806.7) = (1290.7)/(390442.8)`
`R = (390442.8)/(1290.7)`
Total resistance, `R = 302.5 Omega`
Current drawn from the line can now be calculated by using Ohm's law as follows:
`(V)/(I) = R`
`(220)/(I) = 302.5`
`I = (220)/(302.5)`
`I = 0.727 A` or `0.73 A`
Thus, the current drawn from line is 0.73 ampere.