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AP Physics 2
10.6 Capacitors
AdvancedMCQMathematical12.8k
A cross-sectional schematic diagram of a parallel-plate capacitor with top and bottom horizontal metal plates separated by vertical distance d. The space between the plates is divided vertically into two rectangular regions. The left region occupies one-third of the horizontal width and is filled with a shaded dielectric slab labeled with dielectric constant \(\kappa_1\). The right region occupies two-thirds of the horizontal width and is filled with a cross-hatched dielectric slab labeled with dielectric constant \(\kappa_2\). A vertical double-headed arrow on the left indicates the plate separation d. The total plate area is indicated as A. No other labels, lines, text, or axes appear.
Cross section of a parallel-plate capacitor with two side-by-side dielectric slabs.
An ideal parallel-plate capacitor with plate area \(A\) and plate separation \(d\) has capacitance \(C_0\) in a vacuum. The space between the plates is completely filled with two rectangular dielectric slabs placed side-by-side, both spanning the entire separation distance \(d\). Slab 1 has dielectric constant \(\kappa_1\) and covers an area of \(\frac{1}{3}A\), while Slab 2 has dielectric constant \(\kappa_2\) and covers the remaining area of \(\frac{2}{3}A\). What is the total equivalent capacitance of this capacitor in terms of \(C_0\), \(\kappa_1\), and \(\kappa_2\)?

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