A 100 W bulb B1 and two 60 W bulbs B2 and B3 are connected to a 250 V sourc

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Question

A 100 W bulb

B_{1}

and two 60 W bulbs

B_{2}

and

B_{3}

are connected to a 250 V source as shown in figure.

W_{1}

,

W_{2}

and

W_{3}

are the output powers of the bulbs

B_{1}

,

B_{2}

and

B_{3}

respectively then

A 100 W Bulb B1 And Two 60 W Bulbs B2 And B3 Are Connec...

Options:

A . W1> W2 = W3

B . W1> W2> W3

C . W1

D . W1

Answer: Option D
:
D
The resistances of bulbs

B_{1}, B_{2}

and

B_{3}

respectively are

R_{1} \frac{v^{2}}{w_{1}} = \frac{(250)^{2}}{100} = 625

ohm

R_{2} = \frac{(250)^{2}}{60} = 1042

ohm =

R_{3}

Voltage across

B_{3}

is

V_{3} = 250 V

Voltage across

B_{1}

is

V_{1} = \frac{V R_{1}}{(R_{1} + R_{2})} = \frac{250 \times 625}{(625 + 1042)} = 93.7 V

Voltage across

B_{2}

is

V_{2} = 250 - 93.7 = 156.3 V

Power output

W_{1} = \frac{V^{2}}{R_{1}} = \frac{(93.7)^{2}}{625} = 14 W

W_{2} = \frac{(156.3)^{2}}{1042} = 23 w

W_{3} = \frac{(250)^{2}}{1042} = 60 w

Hence

W_{1} < W_{2} < W_{3}

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