In the following figure, \(C_1\) and \(C_2\) are ideal capacitors. \(C_1\) has been charged to 12V before the ideal switch \(S\) is closed at \(t = 0\). The current \(i(t)\) for all \(t\) is
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When dealing with ideal capacitors, the current at \( t = 0 \) after switching can be an impulse if there is a sudden voltage change across the capacitor.
When the switch is closed at \(t = 0\), the current \(i(t)\) will initially be an impulse function due to the sudden change in voltage across the capacitors. Since \(C_1\) is charged, the instantaneous current that flows is a result of this sudden connection, leading to an impulse response. Thus, the correct answer is option (2).
