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Standard VIII
Physics
Question

The circuit given below is for the operation of an industrial fan. The resistance of the fan is 3ohm. The regulator provided with the fan is a fixed resistor and a variable resistor in parallel. Under what value of the variable resistance given, power transferred to the fans will be maximum? The power source of the fan is a dc source with internal resistance of 6ohm
330747_20e8315631444d50ba69afdda458c367.png
  1. 3 Ω
  2. 0
  3. ∞
  4. 6Ω

A
3 Ω
B
0
C
∞
D
6Ω
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Solution
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The power transferred to fan is given as P=V2/R, where R is the total resistance of the circuit. As power is inversely proportional to total resistance. So for maximum power, the total resistance should be minimum. Total resistance here is R=6r6+r+3. r is the variable resistance.
R is minimum when r=0.

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330747_20e8315631444d50ba69afdda458c367.png
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