What is typically observed in a capacitor charging from a direct current supply?

When a capacitor is connected to a direct current (DC) supply, it undergoes a charging process characterized by the behavior of voltage across its plates over time. Initially, when the capacitor is connected to the DC source, it begins in an uncharged state, which means the voltage across its terminals is at zero.

As the capacitor charges, the voltage across it does not increase instantly. Instead, it follows an exponential curve due to the relationship defined by the time constant of the capacitor, which is the product of the resistance (if any in series) and the capacitance. This means that the voltage increases gradually, reaching approximately 63% of the maximum voltage after one time constant. The voltage continues to rise exponentially, approaching the supply voltage asymptotically but never quite reaching it in finite time.

This behavior is governed by the fundamental principles of capacitors and their response to changes in voltage. The time it takes to charge fully depends on these components, and the smooth and continuous increase in voltage reflects the nature of capacitors to store electrical energy over time rather than instantaneously.

In contrast, the other options provided do not accurately describe the behavior of a charging capacitor. A constant voltage refers to a fully charged state, an immediate jump to maximum