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Unformatted text preview: Physics 21 Fall, 2011 Solution to HW-19 29-34 A dielectric of permittivity 3 . 3 10 11 F / m com- pletely fills the volume between two capacitor plates. For t > 0 the electric flux through the dielectric is (7800 V m / s 3 ) t 3 . The dielectric is ideal and nonmagnetic; the conduction cur- rent in the dielectric is zero. At what time does the displace- ment current in the dielectric equal 23 A? For a charging capacitor we have the equation for displace- ment current i D = d E dt . When a dielectric is between the capacitor plates, we multiply by the dielectric constant K to get the permittivity of the material = K . Thus we have i D = d E dt . The function for the electric flux can then be substituted: i D = d dt ( (7800 V m / s 3 ) t 3 ) = (7800 V m / s 3 ) d ( t 3 ) dt = (7800 V m / s 3 )(3) t 2 Solving this for time: t = radicalBigg i D (7800 V m / s 3 )(3) = radicalBigg 23 10 6 3 . 3 10 11 (7800 V m / s 3 )(3) = 5 . 5 s 29-51 As a new electrical engineer for the local power com- pany, you are assigned the project of designing a generator of sinusoidal ac voltage with a maximum voltage of 120 V....
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