Two electric bulbs , rated at (25W,220V) and (100W,220V), are connected in series across a 220 V voltage source , if the 25W and 100W bulbs draw powers `P_(1) and P_(2)` Respectively , then :

Options

A. `P_1 = 16 W`
B. `P_1 = 4W`
C. `P_2 = 16W`
D. `P_2 = 4W`

Answer

A, D

Explanation

a.,d.
`R_1 = V^2/W_1 = (220)^2/25 = (22)^2 xx 4 Omega`
`R_2 = (V^2)/W_2 = (220)^2/100 = (22)^2 Omega`

Current in the circuit when the bulbs are connected in series,
`I = 220/((22)^2 xx 4 + (22)^2) = 10/(22 xx 5) = 1/11 A `
Hence, `P_1 = I^2R_1 = (1/11)^2 xx (22)^2 xx 4 = 16 W`
And `P_2 = I^2R_2 = (1/11)^2 xx (22)^2 = 4W`.