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.
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
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`
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