Electro Magnetic Induction And Alternating Currents Question 206

Question: In an LCR circuit as shown below both switches are open initially. Now switch $ S_{1} $ is closed, $ S_{2} $ kept open. (q is charge on the capacitor and $ \tau =RC $ is Capacitive time constant). Which of the following statements is correct?

Options:

A) At t=0, q=CV (1-e)

B) At $ t=\tau $, $ q=CV/2 $

C) At, $ t=2\tau $ , $ q=CV(1-{{e}^{-2}}) $

D) At, $ t=2\tau $ , $ q=CV(1-{{e}^{-1}}) $

Show Answer

Answer:

Correct Answer: C

Solution:

  • Charge on he capacitor at any time t is given by $ q=CV\text{ (1}-{{e}^{-t/\tau }})att=2\tau $ $ q=CV\text{ (1-}{{\text{e}}^{-2}}\text{)} $


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