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 ≤ t < (2n + 1)T, (n = 0, 1, 2 . . .) S1 to P1 and S2 to P2. For (2n + 1)T ≤ t < (2n + 2)T, (n = 0, 1, 2 . . .) S1 to Q1 and S2 to Q2. Assume that the capacitor has zero initial charge. Give that u(t) is a unit step function, the voltage VC(t) across the capacitor is given by

tu( t ) + 2limits_n = 1^fty ( - 1 )^n( t - nT )u( t - nT )

Network Theory and Analysis

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 ≤ t < (2n + 1)T, (n = 0, 1, 2 . . .) S₁ to P₁ and S₂ to P₂.
For (2n + 1)T ≤ t < (2n + 2)T, (n = 0, 1, 2 . . .) S₁ to Q₁ and S₂ to Q₂.
Assume that the capacitor has zero initial charge. Give that u(t) is a unit step function, the voltage V_C(t) across the capacitor is given by

A) $$\sum\limits_{n = 0}^\infty {{{\left( { - 1} \right)}^n}tu\left( {t - nT} \right)} $$ B) $$u\left( t \right) + 2\sum\limits_{n = 1}^\infty {{{\left( { - 1} \right)}^n}\left( {t - nT} \right)u\left( {t - nT} \right)} $$ C) $$tu\left( t \right) + 2\sum\limits_{n = 1}^\infty {{{\left( { - 1} \right)}^n}\left( {t - nT} \right)u\left( {t - nT} \right)} $$ D) $$\sum\limits_{n = 0}^\infty {\left[ {0.5 - {e^{ - \left( {t - 2nT} \right)}} + 0.5{e^{ - \left( {t - 2n - T} \right)}}} \right]} $$

Answer & Solution

Correct Answer: Option C

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