Multiple choice

The circuit shown in the figure is used to charge the capacitor C alternately from two current sources as indicated. The switches S1 and S2 are mechanically coupled and connected as follows: For 2nT $\le$ t $\le$ (2n + 1) T, (n = 0, 1, 2, ...) S1 to P1 and S2 to P2 For (2n + 1) T $\le$ t $\le$ (2n + 2) T, (n = 0, 1, 2, ...) S1 to Q1 and S2 to Q2

Assume that the capacitor has zero initial charge. Given that u (t) is a unit step function, the voltage vc (t) across the capacitor is given by

  1. $\displaystyle \sum_{n=1}^\infty (-1)^n \ tu \ (t - nT)$
  2. u (t) + 2$\displaystyle \sum_{n=1}^\infty (-1)^n \ u \ (t - nT)$
  3. t u (t) + 2$\displaystyle \sum_{n=1}^\infty (-1)^n \ u \ (t - nT)$(t - nT)
  4. $\displaystyle \sum_{n=1}^\infty [0.5 - e^{-(t-2nT)} + 0.5 e^{-(t-2nT)} ]$
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C Correct answer
Explanation

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