A parallel plate capacitor whose capacitance C is 14 pF is charged by a battery to a potential difference V = 12V between its plates. The charging battery is now disconnected and a porcelain plate with k = 7 is inserted between the plates, then the plate would oscillate back and forth between the plates with a constant mechanical energy of .......... pJ. (Assume no friction)
A parallel plate capacitor whose capacitance C is 14 pF is charged by a battery to a potential difference V = 12V between its plates. The charging battery is now disconnected and a porcelain plate with k = 7 is inserted between the plates, then the plate would oscillate back and forth between the plates with a constant mechanical energy of .......... pJ. (Assume no friction)
Initial charge Q = CV = 14 * 10? ¹² * 12 = 168 * 10? ¹² C
Initial energy U_in = ½ CV² = ½ (14 * 10? ¹²) * 12² = 1008 pJ
When the battery is disconnected and a dielectric (k=7) is inserted, the new capacitance is C' = kC.
The charge Q remains constant.
Final energy U_f = Q²/2C' = Q²/ (2kC) = (CV)²/ (2kC)
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Physics Electrostatic Potential and Capacitance 2025
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