# The zero-input and zero-state response of a circuit consisting only of a dc source and a capacitor?

From my understanding, the zero-input and zero-state responses of an RC circuit can be found by solving for the homogenous and particular solution of the ordinary differential equation found using Kirchhoff's current law. But I am confused as to what happens if there is no resistor in the circuit. In this situation, y(t) = x(t), where x(t) is the voltage input and y(t) is the voltage output across the capacitor. Now, my intuitive understanding tells me that the zero-input response is zero because no current has been provided yet and the capacitor is uncharged. But what about the zero-state response? Since there is no resistor in the circuit, will the capacitor simply not discharge? So, will the zero-state response of the circuit also be zero?

• You'll be dealing with infinites (or machine limits). The source has zero internal resistance. Mar 22, 2021 at 18:00
• Would you mind elaborating a bit on that? Does the source having infinite resistance imply that the zero-state response is 0 since there will be no current? Mar 23, 2021 at 2:15