26.5.2 Charging a Capacitor
All well and good, but how does a capacitor get charged? By connecting it to a battery! FIGURE 26.21a shows the two plates of a capacitor shortly after two conducting wires have connected them to the two terminals of a battery. At this instant, the battery’s charge escalator is moving charge from one capacitor plate to the other, and it is this work done by the battery that charges the capacitor. (The connecting wires are conductors, and you learned in Chapter 22 that charges can move through conductors as a current.) The capacitor voltage steadily increases as the charge separation continues.
FIGURE 26.21 A parallel-plate capacitor is charged by a battery.
NOTE Negative electrons that move from positive to negative are the charge carriers in metal wires. However, you’ll learn in the next chapter that current—as shown in Figure 26.21a—is defined to be the equivalent motion of positive charge from negative to positive. Thinking of current as the motion of positive charges is perfectly adequate from a macroscopic perspective of considering only the consequences of a current.
But this process cannot continue forever. The growing positive charge on the upper capacitor plate exerts a repulsive force on new charges coming up the escalator, and eventually the capacitor charge gets so large that no new charges can arrive. The capacitor in FIGURE 26.21b is now fully charged. In Chapter 28 we’ll analyze how long the charging process takes, but it is typically less than a nanosecond for a capacitor connected directly to a battery with copper wires.
Once the capacitor is fully charged, with charges no longer in motion, the positive capacitor plate, the upper wire, and the positive terminal of the battery form a single conductor in electrostatic equilibrium. This is an important idea, and it wasn’t true while the capacitor was charging. As you just learned, any two points in a conductor in electrostatic equilibrium are at the same potential. Thus the positive plate of a fully charged capacitor is at the same potential as the positive terminal of the battery.
Similarly, the negative plate of a fully charged capacitor is at the same potential as the negative terminal of the battery. Consequently, the potential difference between the capacitor plates exactly matches the potential difference between the battery terminals. A capacitor attached to a battery charges until . Once the capacitor is charged, you can disconnect it from the battery; it will maintain this charge and potential difference until and unless something—a current—allows positive charge to move back to the negative plate. An ideal capacitor in vacuum would stay charged forever.
The keys on computer keyboards are capacitor switches. Pressing the key pushes two capacitor plates closer together, increasing their capacitance. A larger capacitor can hold more charge, so a momentary current carries charge from the battery (or power supply) to the capacitor. This current is sensed, and the keystroke is then recorded.