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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
Rating 100 W; Electric current taken by 220 V lamp -
P1 = VI1
⇒ I1 = `"P"_1/"V"`
= `100/220`
= `5/11` A
Similarly, the rating is 60 W; Value of electric current taken by 220 V electric lamp -
P2 = VI2
⇒ I2 = `"P"_2/"V"`
= `60/220`
= `3/11` A
∴ Total current drawn by the electric mains
I = I1 + I2
= `5/11 + 3/11`
= `8/11` A
= 0.73 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
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