Two lamps, one rated 100 W 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 220 V?
Two lamps, one rated 100 W; 220 V, and the other 60 W; 220 V, are connected in parallel to electric mains supply. Find the current drawn by two bulbs from the line, if the supply voltage is 220 V.
Solution 1
Both the bulbs are connected in parallel. Therefore, potential difference across each of them will be 220 V, because no division of voltage occurs in a parallel circuit.
Current drawn by the bulb of rating 100 W is given by,Power = Voltage x Current
Current = Power/Voltage = 60/220 A
Hence, current drawn from the line = 100/220 + 60/220 = 0.727 A
Solution 2
For first bulb:
P = 100 W, V = 220V
As we know, P = `v^2/R`
Thus, resistance of first bulb, `R_1 = v^2/P = 220^2/100` = 484 Ω
For second bulb:
Thus, resistance of second bulb, `R_2 = v^2/P = 220^2/60` = 806.67 Ω
Since, the two bulbs are connected in parallel, therefore
Total resistance = `(R_1R_2)/(R_1 + R_2) = (484xx806.67)/(484+806.67)` = 302.5 Ω
Hence, the current drawn by two bulbs is
I = `220/302.5 = 0.73 A`
