Question

Bulb B1(40W, 220V) connected to a 220V supply glows with some brightness. Predict the change in brightness(if any) with reason if another identical bulb B2(40W, 220V) is connected in:-
(a) Series to B1
(b) Parallel to B1

Answer 1

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.
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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.
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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.