Question 16.12: CAPA CITORS WITH TWO DIELECTRICS GOAL Derive a symbolic expr...
CAPA CITORS WITH TWO DIELECTRICS
GOAL Derive a symbolic expression for a parallel-plate capacitor with two dielectrics.
PROBLEM A parallel-plate capacitor has dielectrics with constants \kappa_{1} and \kappa_{2} between the two plates, as shown in Figure 16.29. Each dielectric fills exactly half the volume between the plates. Derive expressions for (a) the potential difference between the two plates and (b) the resulting capacitance of the system.
STRATEGY The magnitude of the potential difference between the two plates of a capacitor is equal to the electric field multiplied by the plate separation. The elec tric field in a region is reduced by a factor of 1 / \kappa when a dielectric is introduced, so E=\sigma / \epsilon=\sigma / \kappa \epsilon_{0}. Add the potential difference across each dielectric to find the total potential difference \Delta V between the plates. The voltage difference across each dielectric is given by \Delta V=E d, where E is the electric field and d the displacement. Obtain the capacitance from the relationship C=Q / \Delta V.
Our explanations are based on the best information we have, but they may not always be right or fit every situation.
Learn more on how we answer questions.