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Q.

A 100 W bulb B1 and two 60 W bulbs B2 and B3, are connected to a 250 V source, as shown in the figure. Now W1, W2 and W3 are the output powers of the bulb B1, B2 and B3 respectively. Then,

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a

W1>W2 = W3

b

W1>W2 > W3

c

W1

d

W1

answer is D.

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Detailed Solution

Let the given power ratings be defined at an operating voltage V. The resistances of the three bulbs are given by R1 = V2100 ,  R2 = V260 ,  R3 = V260 . In the given configuration, the current through  B1  and  B2  is i=250R1+R2=250V2100+V260  = 250V2(100×60100+60)  = 250V2(752) Substitute the values of  i ,  R1 , and  R2  to get the output powers  W1 = i2 R1 ≈ 250V2×7522V2100=2502V47522V2100=14  250V2 ,  W2 = i2 R2 ≈250V2×7522V260=2502V47522V260=23  250V2 ,  and W3 = 2502R3 = 60 ( 250V)2
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A 100 W bulb B1 and two 60 W bulbs B2 and B3, are connected to a 250 V source, as shown in the figure. Now W1, W2 and W3 are the output powers of the bulb B1, B2 and B3 respectively. Then,