Consider a spherical capacitor with two layers of dielectric materials. The inner conductor radius is a and the outer conductor radius is c. The inner dielectric material fills the thickness (b-a) and its permittivity is ε₁ and the outer dielectric material fills the thickness (c-b) and its permittivity is 2. Find the capacitance of the capacitor.
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- A capacitor is formed from two concentric spherical conducting shells separated by vacuum. The inner sphere has radius 10.0 cm , and the outer sphere has radius 16.5 cm . A potential difference of 140 V is applied to the capacitor. What is the energy density at r= 10.1 cm , just outside the inner sphere? What is the energy density at r = 16.4 cm , just inside the outer sphere?Determine the equivalent capacitance between points a and b for the combination of capacitors shown in (Figure 1). Express your answer in terms of the variables C1, C2, C3, and C4Suppose a capacitor consists of two coaxial thin cylindrical conductors. The inner cylinder of radius ra has a charge of +Q, while the outer cylinder of radius ry has charge -Q. The electric field E at a radial distance r from the central axis is given by the function: E = aer/a0 + B/r + bo where alpha (a), beta (8), an and bo are constants. Find an expression for its capacitance. First, let us derive the potential difference Vah between the two conductors. The potential difference is related to the electric field by: Vah = Edr= - Fdr Calculating the antiderivative or indefinite integral, Vab = (-aager/a0 +8 + bo By definition, the capacitance Cis related to the charge and potential difference by: C = Evaluating with the upper and lower limits of integration for Vab, then simplifying: C= Q/( (e"b/a0 .eralao) + B In( )+ bo ( ))
- Consider the combination of capacitors below: C2 (a) If the capacitance of C, and C2 are the same, C3 has capacitance of 9.3 mF, and the capacitor network has equivalent capacitance of 3.0 mF, determine the capacitance of the unknown capacitors. Give your answer in units of mF.What is the equivalent capacitance of a 1 Farad capacitor and a 0.5 Farad capacitor in parallel?Part A and Part B please A capacitor is formed from two concentric spherical conducting shells separated by vacuum. The inner sphere has radius 12.0 cm, and the outer sphere has radius 15.0 cm. A potential difference of 110 V V is applied to the capacitor. Part A What is the energy density at r = 12.1 cm, just outside the inner sphere? Part B What is the energy density at r = 14.9 cm, just inside the outer sphere?
- Calculate the equivalent capacitance for the configurations Y and Z which are shown below. The values of the capacitances in the figure are in µ F. Then rank X, Y, and Z in order of INCREASING equivalent capacitance. 13.0 10.8 6.3 3.8 37.0 X' Y' Z* Smallest capacitance has rank 1, largest capacitance has rank 3. 1 The rank of X is ... 3 The rank of Y is ... 2 The rank of Z is ... Submit Answer Incorrect. Tries 3/5 Previous TriesDetermine which df th following equations can be eigen function equation and qive tk values an sinfx) dx 2 d? sin TTX 2 dx2 a x uP +) -ih 으 ek T 2ikyA parallel plate capacitor has a charge Q, and a voltage difference AV. The gap is air-filled with an electric field E. 1. The capacitor is then disconnected from the circuit so that there is no path for the electrons to move from one plate to another. An insulator of dielectric constant *> 1 is then inserted to fill the entire gap. The electric field in the gap will cause the charges in the dielectric to separate slightly. This leaves an excess layer of negative charges on the top of the insulator and an excess layer of positive charges at the bottom surface of the insulator. This induced surface charge creates an induced electric field opposite the direction of the original electric field. a. The new net electric field is Ē' = Z₂ + Ēinduced. Which is true of E', the magnitude of the new net field? Choose one. E' = E, (the net electric field is the same as the original electric field) E' = E₁/x (the net electric field is smaller than the original field.) b. Which is true of the new…
- Consider a cylindrical capacitor with two layers of dielectric materials. The inner conductor radius is a and the outer conductor radius is c. The inner dielectric material fills the thickness (b-a) and its permittivity is & and the outer dielectric material fills the thickness (c-b) and its permittivity is ε, as shown in the figure. Find the capacitance of the capacitor if its length is 1. Consider a spherical capacitor with two layers of dielectric materials. The inner conductor radius is a and the outer conductor radius is c. The inner dielectric material fills the thickness (b-a) and its permittivity is & and the outer dielectric material fills the thickness (c-b) and its permittivity is ६, Find the capacitance of the capacitor.A parallel-plate capacitor has square plates of edge length 0.9 cm and a plate spacing of 0.029 mm. If the gap between the plates is a vacuum, what is the capacitance? FThe diagram below depicts a cross section of coaxial conductor with an inner wire of diameter di and an outer conducting sheath of inside diameter do, and some material placed in the space between the two wires. Suppose that you have a coaxial wire with di=1.3 mm and do=7.55 mm, and we put mylar (κ=3.1) in the space between the two wires. If there is a potential of 1 kV between the wires, how much energy is stored in a 10 m piece of cable? For my answer I got 5.32 J which was wrong.