Question

In fundamentals of physics book by Resnick and Haliday it has been written that the electric field of the battery drives electron from the positive plate of the capacitor and pushes electrons to the negative plate. At one point when the potential of positive terminal of battery becomes equal to the potential of positive plate of capacitor,there won't be any electric field in the wire to push charges. But in circuits,we know that all the points are in same potential in a resistance less wire,still current flows through the wire. In this case also the two potentials have become equal. So why no flow of current in this case?

Answer 1

Current ceases to flow to a capacitor when it reaches the same potential as the battery because the potential difference becomes zero, eliminating the electric field required to move charges. In contrast, a resistance-less wire connected to a battery maintains a constant potential difference and electric field which allows current to continue flowing.

Step-by-step explanation:

The question asked pertains to why there is no current flow in a capacitor circuit when the potential of the positive terminal of the battery becomes equal to the potential of the positive plate of the capacitor, despite there still being current flow in a resistance-less wire where all points are at the same potential. To understand this, it's key to consider the fact that in a circuit, current flows due to a potential difference. Initially, electrons flow from the negative to the positive side because the battery has a higher potential than the uncharged capacitor.

As the capacitor charges, the voltage across it (Vc = Q/C, where Q is the charge and C is the capacitance) increases until it equals the electromotive force (emf) of the battery. At this point, the potential difference between the capacitor and the battery becomes zero, and no further current flows to the capacitor because there is no driving force (electric field) to move the charges. Kirchhoff's second rule (the loop rule) supports this, stating that the algebraic sum of potential changes in a closed loop is zero, which means that when the capacitor is fully charged, the potential around the loop is balanced.

However, in a resistor-less wire connected to a battery, there is still a potential difference provided by the battery which maintains a constant electric field in the wire, causing current to flow despite the wire having uniform potential. In contrast, once the capacitor reaches the same potential as the battery, no such source-driven electric field exists between them, and thus, the current ceases.