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Physics-

General

Easy

Question

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 bulbs B₁, B₂ and B₃, respectively. Then

$W_{1} > W_{2} = W_{3}$
$W_{1} > W_{2} > W_{3}$
$W_{1} < W_{2} = W_{3}$
$W_{1} < W_{2} < W_{3}$

The correct answer is: $W subscript 1 end subscript less than W subscript 2 end subscript less than W subscript 3 end subscript$

$P equals fraction numerator V to the power of 2 end exponent over denominator R end fraction$ so $R equals fraction numerator V to the power of 2 end exponent over denominator P end fraction$ Þ $R subscript 1 end subscript equals fraction numerator V to the power of 2 end exponent over denominator 100 end fraction$ and $R subscript 2 end subscript equals R subscript 3 end subscript equals fraction numerator V to the power of 2 end exponent over denominator 60 end fraction$
Now $W subscript 1 end subscript equals fraction numerator left parenthesis 250 right parenthesis to the power of 2 end exponent over denominator left parenthesis R subscript 1 end subscript plus R subscript 2 end subscript right parenthesis to the power of 2 end exponent end fraction. R subscript 1 end subscript$ , $W subscript 2 end subscript equals fraction numerator left parenthesis 250 right parenthesis to the power of 2 end exponent over denominator left parenthesis R subscript 1 end subscript plus R subscript 2 end subscript right parenthesis to the power of 2 end exponent end fraction. R subscript 2 end subscript$
and $W subscript 3 end subscript equals fraction numerator left parenthesis 250 right parenthesis to the power of 2 end exponent over denominator R subscript 3 end subscript end fraction$
$W subscript 1 end subscript colon W subscript 2 end subscript colon W subscript 3 end subscript equals 15 colon 25 colon 64$ or $W subscript 1 end subscript less than W subscript 2 end subscript less than W subscript 3 end subscript$

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