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Learn about capacitance in this chapter, covering topics such as calculating capacitance for different geometries, connecting capacitors, energy storage, and behavior of dielectrics in electric fields. Explore Gauss' law with dielectrics and how capacitance is affected by charge and potential difference changes.
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Chapter 25 Capacitance In this chapter we will cover the following topics: -Capacitance C of a system of two isolated conductors. -Calculation of the capacitance for some simple geometries. -Methods of connecting capacitors (in series, in parallel). -Equivalent capacitance. -Energy stored in a capacitor. -Behavior of an insulator (a.k.a. dielectric) when placed in the electric field created in the space between the plates of a capacitor. -Gauss’ law in the presence of dielectrics. (25-1)
q = CV q V- V+ V O ) (25-2)
Checkpoint 1: • Does the capacitance C of a capacitor increase, decrease, or remain the same • When the charge q on it is doubled and • When the potential difference V across it is tripled? The capacitance of the capacitor depends only on the geometry of the plates and not on their charge or potential difference.
V -_ + (25-3)
-q +q -q +q (25-4)
V- V+ (25-5)
P S N (25-6)
S (25-7)
S (25-8)
Checkpoint 2: • For capacitors charged by the same battery, does the charge stored by the capacitor increase, decrease, or remain the same in each of the following situations? • The plate separation of a parallel-plate capacitor is increased. • The radius of the inner cylinder of a cylindrical capacitor is increased • The radius of the outer spherical shell of a spherical capacitor is increased
Checkpoint 3: • A battery of potential V stores charge q on a combination of two identical capacitors. What are the potential difference across and the charge on either capacitor if the capacitors are • In parallel • In series ?
-q' q' - + dq' - + - + - + - + V' Charge A q q' Voltage B O V V' (25-13)
-q q - + - + - + A A - + - + d (25-14)
q V -q q' V -q' V q -q V' q -q (25-15)
q V -q q' V -q' V q -q V' q -q (25-16)
conductor dielectric q (25-17)