Q.
The resistance of the filament of an electric bulb changes with temperature. If an electric bulb rated 220 volt and 100 watt is connected to a (220 x .8) volt source, then the actual power would be
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a
100 × 0.8 watt
b
100 × 0.82 watt
c
between 100 x 0.8 watt and 100 watt
d
between 100 x (0.8)2 watt and 100 x 0.8 watt
answer is D.
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Detailed Solution
P1= 2202R1 and P1= 220 × 0.82R2P2P1 = 220 × 0.822202 × R1R2⇒ P2P1 = 0.82 × R1R2Here R2 < R1(because voltage decreases from 220 V → 220 x 0.8 V. It means heat produced → decreases)So R1R2 > 1 ⇒ P2 0.82 P1 ⇒ P2 > 0.82 × 100 WAlso P2P1 = 220 × 0.8i2220 i1, Since i2 < i1 we expectSo P2P1 < 0.8 ⇒ P2 < 100 × 0.8Hence, the actual power would be between 100 x (0.8)2 W and (100 x 0.8) W
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