A capacitor offers infinite resistance at steady state because, in a DC (direct current) circuit, once it is fully charged, it acts as an open circuit to the steady flow of current. This occurs because a capacitor charges and stores electrical energy in the form of an electric field between its plates. As the capacitor charges, the voltage across it increases until it equals the applied voltage of the DC source. At this point, the capacitor stops allowing current to pass through it, effectively presenting infinite resistance to the DC steady-state current. This behavior contrasts with resistors, which offer a constant resistance value regardless of the steady-state conditions.

In a steady-state DC circuit, a fully charged capacitor behaves as if it has infinite resistance because it no longer permits current to flow through it. Once the capacitor reaches its fully charged state, the current ceases to flow, and the only current that may exist is leakage current, which is minimal in ideal capacitors. Therefore, in a steady-state condition, the resistance offered by a capacitor to direct current is very high, approaching infinity.

When a capacitor is in steady state, it has reached equilibrium where the voltage across its terminals remains constant and no further charging or discharging occurs. In this state, the capacitor behaves as an open circuit to direct current because it has stored the maximum charge it can hold for the applied voltage. This characteristic makes capacitors useful for filtering out DC components from signals or blocking DC current flow in circuits designed for AC (alternating current) operation.

Capacitors block signals at steady state by offering infinite resistance to DC currents once they are fully charged. In AC circuits, however, capacitors pass AC signals while blocking DC signals due to their ability to charge and discharge with the alternating voltage cycles. This property allows capacitors to selectively pass certain frequencies of signals, making them essential in applications such as coupling capacitors in amplifiers, signal processing circuits, and power supply filtering.

In electrical circuits, infinite resistance typically occurs in situations where a component or connection is open, meaning there is no continuous path for current to flow. This can be due to a component failure, an open switch, or a deliberate design feature such as in the case of a capacitor in steady state. Infinite resistance effectively stops the flow of current in that part of the circuit, preventing normal operation until the issue is resolved or the circuit configuration changes. Understanding and managing resistance characteristics in circuits is crucial for ensuring reliable and efficient electrical performance in various applications.