A parallel plate capacitor with plate separation d is connected to a battery. Th

Question

A parallel plate capacitor with plate separation d is connected to a battery. The capacitor is fully charged to Q Coulombs and a voltage of V. (C is the capacitance and U is the stored energy.) Answer the following questions regarding the capacitor charged by a battery. For each statement below, select True or False. With the capacitor connected to the battery, increasing d increases C. With the capacitor connected to the battery, decreasing d increases U. After being disconnected from the battery, inserting a dielectric with ? will increase U. After being disconnected from the battery, inserting a dielectric with ? will increase V. After being disconnected from the battery, inserting a dielectric with ? will decrease C. After being disconnected from the battery, increasing d increases V.

Explanation / Answer

You need to use a few formulas, one for capacitance, one for energy in a charged capacitor, and one that relates voltage and stored charge in a capacitor Eq 1: C= k*epsilon0*A/d where: k = relative dielectric constant of dielectric layer epsilon0 = permittivity of vacuum A = area of the plates d = spacing between plates Eq. 2: U = 1/2*C*V^2 where: C= capacitance (in Farads) V = Voltage Q = Coulombs U = energy (in joules) Eq. 3: Q = C*V A. Rearranging Eq. 3, V = Q/C. Once disconnected, Q is fixed. From first formula, increasing A increases C, so V must decrease. B. The battery will keep capacitor voltage constant. From Eq. 1, decreasing d increases C. From Eq. 2, this means that U must increase if V is held constant. C. From Eq. 2, increasing d decreases C. Being connected to battery does not matter. D. From Eq 1, decreasing d increases C. Since V is constant (cap connected to battery), from Eq. 3, Q must increase. E. Once we disconnect the capacitor from the battery, U stays constant - (from Conservation of Energy). Although increasing A causes V to decrease (see question A above), the energy of the system stays constant. F. Similar to question C above. From Eq. 1, increasing A increases C.

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