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A battery of 10 V is connected to a resistance of 20 Ω through a variable resistance R . If the variable resistance R is increased at the rate of 5 Ω min - 1 , then the amount of charge that passes through the battery in 4 min is

Options

  1. A120   C
  2. B120 log e 2   C
  3. C120 log e 2   C
  4. D60 log e 2   C

Correct answer

B. 120 log e 2   C

Step-by-step solution

Q = ∫ i dt = ∫ V R dt = ∫ 0 240 10 20 + 5 60 t dt t converted in seconds = 10 5 60 ln ⁡ 5 60 t + 20 0 240 = 600 5 ln ⁡ 40 20 = 120 ln ⁡ 2

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