B1 : Rated values : P1 = 40W and V1 = 220 V
R1 = V1² / P1 = 220 * 220 / 40 = 1210 Ω
I1 = P1/V1 = 2/11 A = rated current
Bright is dependent on the power dissipated by the bulb. ie., on I^2 R or V^2/R.
B2 : also has same rated values. P2 = 40 W, V2= 220 V,
R2 = 1210 Ω and I2 = 2/11 A.
a) Now, two bulbs are in series. Both are equivalent.
Voltage = V1' = 220/2 = 110 V Current I1'= 110 / 1210 = 1/11 A
So power dissipated through a bulb = V1' * I1' = 10 W
As Voltage becomes 1/2 V1, power becomes 1/4 th P1. So the bulb glows with much reduced brightness.
b) If the bulbs are connected in parallel, as the case is usually in real life, each bulb draws : 220 Volts and current of 2/11 Amp which are rated values.
Hence the bulbs will glow at their rated brightnesses.