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Current Electricity question

2024 · 31 Jan · Shift 2 · Q68
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Current Electricity question

2024 · 31 Jan · Shift 2 · Q68

JEE MainPhysicsCurrent ElectricityMCQ+4 / −1
By what percentage will the illumination of the lamp decrease if the current drops by 20%?
  1. A
    26%
  2. B
    36%
  3. C
    46%
  4. D
    56%
View written solutionFree

Correct answer: B

  1. Relation between illumination and power

For a lamp, illumination is proportional to the electrical power consumed.

P=I2RP = I^2 RP=I2R

Assuming the resistance RRR of the lamp remains constant, power is proportional to the square of current:

P∝I2P \propto I^2P∝I2

  1. Current drops by 20%

If the initial current is III, then the new current is

I′=0.8II' = 0.8II′=0.8I

  1. New power of the lamp

P′=(I′)2R=(0.8I)2R=0.64I2RP' = (I')^2 R = (0.8I)^2 R = 0.64 I^2 RP′=(I′)2R=(0.8I)2R=0.64I2R

So,

P′=0.64PP' = 0.64PP′=0.64P

  1. Decrease in illumination

The fractional decrease is

P−P′=P−0.64P=0.36PP - P' = P - 0.64P = 0.36PP−P′=P−0.64P=0.36P

Thus, percentage decrease is

0.36×100=36%0.36 \times 100 = 36\%0.36×100=36%

  1. Option matching

The correct option is:

B: 36%

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