Capacitors Oppose A Change In
Capacitor does not oppose a change in voltage. Whereas resistors allow a flow of electrons through them directly proportional to the voltage drop capacitors oppose changes in voltage by drawing or supplying current as they charge or discharge to the new voltage level.

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How does capacitor oppose sudden chane in voltage.

Capacitors oppose a change in. The capacitor oppose the change in voltage by supplying or drawing current. How does inductor oppose sudden change in current. The time depends on the size of the capacitor.
The capacitor resists momentary changes in voltage by sinking some charge when the voltage is momentarily high or sourcing some charge when the voltage is momentarily low. Capacitor oppose a changein voltage across them by supply current as they discharged or charged. The higher the frequency of voltage changes the more current that the capacitor can source or sink before the accumulated charge becomes significant.
The statement that capacitors resist changes in voltage is a relative thing and is time dependent. Capacitor current is proportional the rate of voltage change across it proportional to how quickly the voltage across capacitor is changing. A larger capacitor will take longer to dischargecharge than a small one.
The flow of current through a capacitor in thus directly proportional to the rate of change of voltage across it. Capacitors do not behave the same as resistors. We know that the current flowing through the capacitance in ac circuits is in opposition to the rate of change of the applied voltage but just like resistors capacitors also offer some form of resistance against the flow of current through the circuit but with capacitors in ac circuits this ac resistance is known as reactance or more commonly in capacitor circuits capacitive reactance so capacitance in ac circuits suffers from capacitive reactance.
Capacitors resist changes in voltage because it takes time for their voltage to change. This is given by the relation icdedt where dedt is the instantaneous change in voltage. An instantaneous change in the voltage across a capacitor would require that the rate of change of the voltage dvdt be infinite and hence the current would have to be infinite.
As you must know when a voltage source is connected across the capacitor at t0 it acts as a short circuit and allows all current to flow through that path.

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