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CourseNotes.24

# CourseNotes.24 - can treat this single capacitor as being...

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Figure 18: A Variable Capacitor parallel-plate capacitors connected in parallel. The capacitance of one of the identical capacitors is given by C = 0 A d The capacitance of the entire arrangement is hence C tot = 7 0 A d = 2 . 28 pF Problem 25.48 Figure 19 shows a parallel-plate capacitor with plate area A = 5 . 56 cm 2 and separation distance d = 5 . 56 mm . The left half of the gap is filled with material of dielectric constant κ 1 = 7 . 0; the right half is filled with material of dielectric constant κ 2 = 12 . 0. What is the capacitance? Figure 19: A Capacitor with Two Different Dielectric Slabs Since the plates of a parallel plate capacitor are conductors and conductors are always equipo- tentials, the potential on each side of the capacitor must be the same. The charge therefore will not be the same on both sides unless κ 1 = κ 2 . Since the potential is the same on both sides, we
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Unformatted text preview: can treat this single capacitor as being made up of two capacitors in parallel. This is the reverse of taking two parallel capacitors and treating them as one capacitor. Since they are in parallel, the capacitance will be C = C 1 + C 2 = κ 1 ± A 2 d + κ 2 ± A 2 d = ( κ 1 + κ 2 ) ± A 2 d = 8 . 41 pF Problem 25.62 In ﬁgure 20, the battery potential diﬀerence V is 10 V and each of the seven capacitors has capacitance 10 μF . What is the charge on (a) capacitor 1 and (b) capacitor 2? Capacitor 1 is very straightforward. It has one plate wired directly to the positive side of the battery and the other wired directly to the negative side of the battery. The potential diﬀerence across it must therefore be V . Hence, q 1 = C 1 V = 1 × 10 4 C 24...
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