A certain capacitor has rectangular plates 40 cm by 27 cm, and the gap width is 0.20 mm. If the gap is filled with a material whose dielectric constant is 2.1, what is the capacitance?

It turns out that the dielectric k constant increases the capacitance by a factor of k.  That is, Cnew=kCold.  In this case, with the capacitor not connected to a battery, by what factor does the voltage difference across the capacitor change?

Consider a cylindrical capacitor with inner radius r1 = 8.1 cm, outer radius r2 = 14.3 cm, and length L = 16.7 cm. A dielectric with dielectric constant κ = 53 fills the volume between the two cylinders. The capacitor is connected to a 106.6 V battery and is fully charged. What is the charge on the capacitor? Express your answer in Coulombs to 3 significant figures.

A parallel-plate capacitor is constructed by filling the space between two square plates with a block of three dielectric materials, as shown in the figure below. You may assume that ℓ ≫ d. A parallel-plate capacitor is comprised of two square plates with sides of length ℓ and separation distance d. There are three dielectric materials in the space between the capacitor plates. A material with length ℓ⁄2, height d, and dielectric constant ?1 fills the left half of the space. A material with length ℓ⁄2, height d⁄2, and dielectric constant ?2 fills the top right quarter of the space. A material with length ℓ⁄2, height d⁄2, and dielectric constant ?3 fills the bottom right quarter of the space.   (a) Find an expression for the capacitance of the device in terms of the plate area A and d, ?1, ?2, and ?3. (Use the following as necessary: ?1, ?2, ?3, ?0, A and d.)C =        (b) Calculate the capacitance using the values A = 1.30 cm2, d = 2.00 mm, ?1 = 4.90, ?2 = 5.60, and ?3 = 2.50.

A system of capacitors is shown below. What is the equivalent capacitance of the system is the individual capacitors are; Express the answer in microFarads. For example, if the answer came out to be 4.98 X 10-7 F, this is the same as 49.8 microFarads. You would then answer with the numeric value of 4.98. C1 = 5.5 x 10-6 F C2 = 5.7 x 10-6 F C3 = 8 x 10-6 F C4 = 4.5 x 10-6 F C5 = 2.1 x 10-6 F

A capacitor is attached to a battery. It has initial capacitance Co, voltage Vo, charge Qo, and energy Uo. Let's put some dielectric material of dielectric constant K in there in two different ways. For each case, figure out the following for the resulting "new" capacitor: C, V, Q, and U, in terms of the old value and K. The capacitor is left attached to the battery. A slab of dielectric material with K=3 is inserted into the capacitor without otherwise disturbing it. In terms of the initial values, what are the new values? The capacitor is disconnected from the battery after it is charged up to Qo. Then, a slab of dielectric material with K=3 is inserted into the capacitor without anybody touching the plates or otherwise disturbing the capacitor. In terms of the initial values, what are the new values?

Cylindrical conducting surfaces with relative permittivity of 390 are used as plates of a capacitor. It has a thickness of 3.24 mm and a radius of 4.6 cm. What is the energy stored in this capacitor if a voltage of 362 V is applied?

A system of capacitors is shown below. What is the equivalent capacitance of the system is the individual capacitors are; Express the answer in microFarads. For example, if the answer came out to be 4.98 X 10-7 F, this is the same as 49.8 microFarads. You would then answer with the numeric value of 4.98. C1 = 6.7 x 10-6 F C2 = 4.2 x 10-6 F C3 = 2.1 x 10-6 F C4 = 2.6 x 10-6 F C5 = 6.3 x 10-6 F

Units and answer?

What is the equivalent capacitance of a 1 Farad capacitor and a 0.5 Farad capacitor in parallel?