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Definition of Capacitance

Consider two conductors carrying charges of equal magnitude but of opposite sign, as shown in Figure 26.1. Such a combination of two conductors is called a capacitor. The conductors are called plates. A potential difference ΔV exists between the conductors due to the presence of the charges. Because the unit of potential difference is the volt, a potential difference is often called a voltage. We shall use this term to describe the potential difference across a circuit element or between two points in space. What determines how much charge is on the plates of a capacitor for a given voltage? In other words, what is the capacity of the device for storing charge at a particular value of ΔV ? Experiments show that the quantity of charge Q on a capacitor is linearly proportional to the potential difference between the conductors; that is, Q ∝ ΔV The proportionality constant depends on the shape and separation of the conductors. We can write this relationship as Q = CΔV if we define capacitance as follows:

The capacitance C of a capacitor is the ratio of the magnitude of the charge on either conductor to the magnitude of the potential difference between them: Note that by definition capacitance is always a positive quantity. Furthermore, the potential difference ΔV is always expressed in Equation 26.1 as a positive quantity. Because the potential difference increases linearly with the stored charge, the ratio Q /ΔV is constant for a given capacitor. Therefore, capacitance is a measure of a capacitor’s ability to store charge and electric potential energy.
From Equation 26.1, we see that capacitance has SI units of coulombs per volt. The SI unit of capacitance is the farad (F), which was named in honor of Michael Faraday: The farad is a very large unit of capacitance. In practice, typical devices have capacitances ranging from microfarads (10–6 F) to picofarads (10–12 F). For practical purposes, capacitors often are labeled “mF” for microfarads and “mmF” for micromicrofarads or, equivalently, “pF” for picofarads. Let us consider a capacitor formed from a pair of parallel plates, as shown in Figure 26.2. Each plate is connected to one terminal of a battery (not shown in Fig. 26.2), which acts as a source of potential difference. If the capacitor is initially uncharged, the battery establishes an electric field in the connecting wires when the connections are made. Let us focus on the plate connected to the negative terminal of the battery. The electric field applies a force on electrons in the wire just outside this plate; this force causes the electrons to move onto the plate. This movement continues until the plate, the wire, and the terminal are all at the same electric potential. Once this equilibrium point is attained, a potential difference no longer exists between the terminal and the plate, and as a result no electric field is present in the wire, and the movement of electrons stops. The plate now carries a negative charge. A similar process occurs at the other capacitor plate, with electrons moving from the plate to the wire, leaving the plate positively charged. In this final configuration, the potential difference across the capacitor plates is the same as that between the terminals of the battery.

Suppose that we have a capacitor rated at 4 pF. This rating means that the capacitor can store 4 pC of charge for each volt of potential difference between the two conductors. If a 9-V battery is connected across this capacitor, one of the conductors ends up with a net charge of –36 pC and the other ends up with a net charge of +36 pC.

PMT Physics Study Material
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