The voltage on a capacitor does not change immediately because it depends on the accumulation of electric charge on its plates, which takes time. The relationship is described by the equation I = C * dV/dt, indicating that if the time interval (dt) is infinitesimally small, the change in voltage (dV/dt) and thus the current (I) can become infinitely high. Similarly, for inductors, the voltage is related to the rate of change of current, expressed as V = L * dI/dt, which also implies that an instantaneous change in current would result in an infinite voltage. When a DC current is suddenly interrupted in an inductor, it can generate a spark as it attempts to maintain the current flow. Understanding these principles is crucial for grasping the behavior of capacitors and inductors in electrical circuits.
