capacitances gives the result for the series case L L L 2 1 2 2 1 1 2 1 1 1 1 C

Capacitances gives the result for the series case l l

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capacitances, gives the result for the series case: L L L + + = + + = + + = 2 1 2 2 1 1 2 1 / 1 / 1 / 1 / / / C C C C q C q C q V V V tot tot tot tot
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Results for Capacitor Combinations Capacitors in parallel: L + + = 2 1 C C C tot Capacitors in series: L + + = 2 1 / 1 / 1 / 1 C C C tot
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Example: Problem 25-8 What is effective capacitance of the device?
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C 12 F C F C F C μ μ μ 0 . 4 0 . 5 10 3 2 1 = = = F C C C C μ 3 . 3 3 / 10 10 / 3 5 / 1 10 / 1 / 1 / 1 / 1 12 2 1 12 = = = + = + = F C C C tot μ 3 . 7 4 3 . 3 3 12 = + = + =
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Dielectric Materials Applied electric field polarizes material This produces an induced surface charge This reduces field within material This reduces potential difference This increases capacitance Effect of placing a dielectric between the plates of a charged capacitor:
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E=0 electron nucleus Polarization of atoms and molecules Non-polar molecules: induced dipoles Polar molecules: preferential orientation
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Dielectric materials Dielectric materials polarize under external electric field E 0 Polarization creates the opposing electric field: –E’ Total field E=E 0 -E =E 0 / κ < E 0 κ is called dielectric constant It shows how the field in a dielectric is weaker than in vacuum
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Dielectric Constant So the effect of a dielectric is to decrease the field and increase the capacitance.
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