Question

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.

Answer 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

Answer 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