Question

4.2 Dielectric materials used in the manufacture of capacitors are characterized bv conductivities that are small but not zero. Therefore, a charged capacitor loses its charge by slowly leaking across the dielectric. Consider a parallel-plate capacitor with plate spacing d and area A. The volume between the plates is filled with material having dielectric constant K but also with finite resistivity ρ a. What is the capacitance C, in terms of eo, K, A and d? b. What is the resistance of the capacitor, r, in terms of ρ, A and d? c. We can model this real capacitor as an ideal capacitor C in parallel with a resistance r. If the capacitor is charged to Qo and the battery is then disconnected, after what time will the charge on the capacitor have fallen to Qo/4? Now consider an infinitesimal time interval dt at time t during the discharging of the capacitor, write an expression for the energy dissipated through the resistor during the time interval dt in terms Qo, r, C, t and dt Integrate the expression you obtained above to derive an expression for the total energy dissipated through the resistor during the time required for all the charge in the capacitor to leak out How much energy was stored in the capacitor when it was fully charged to Qo ? How does this value compare with the answer you obtained for part e above? d. e. f.

Answer 1