'Incandescent' બલ્બના ફિલામેન્ટનો અવરોધ તાપમાન વધતા વધે છે. જો રૂમના તાપમાને $100\ W, 60\ W$ અને $40\ W$ ના બલ્બના અવરોધ $R_{100}, R_{60}$ અને $R_{40}$ હોય તો...

Question

A$\frac{1}{{{R_{100}}}}\,\, = \,\,\frac{1}{{{R_{40}}}} + \frac{1}{{{R_{60}}}}$
B$R_{100} = R_{40} + R_{60}$
C$R_{100}> R_{60} > R_{40}$
D$\frac{1}{{{R_{100}}}} > \frac{1}{{{R_{60}}}} > \frac{1}{{{R_{40}}}}$

Medium

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Solution

d
$100\,\, = \,\,\frac{{{V^2}}}{{{R_{100}}}}$ $ \Rightarrow \,\,\frac{1}{{{R_{100}}}}\,\, = \,\,\frac{{100}}{{{V^2}}}\,;\,\,$

$60\,\, = \,\,\frac{{{V^2}}}{{{R_{60}}}}\,\,$ $\,\,\frac{1}{{{R_{60}}}}\,\, = \,\,\frac{{60}}{{{V^2}}};\,\,$

$40\,\, = \,\,\frac{{{V^2}}}{{{R_{40}}}}\,$ $\, \Rightarrow \,\,\frac{1}{{{R_{40}}}}\,\, = \,\,\frac{{40}}{{{V^2}}};$

ઉપરના સમીકરણો પરથી $\,\frac{1}{{{R_{100}}}} > \frac{1}{{{R_{60}}}} > \frac{1}{{{R_{40}}}}$

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