A capacitor is constructed of two parallel plates of side l separated by a distance d. A material of dielectric constant k is inserted a distance x as shown in the figure. The potential difference between the plates is V. The energy stored by the system is:
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- What is the capacitance of a parallel plate capacitor in vacuum? Sol. The basic definition for capacitance is: C = Since the electric potential can also be written as V = Ed Where, E is the electric field contribution of the parallel plate (two plane charge): = ol E0 %3D Sigma is the surface charge density given by: O= By, substitution, we get the capacitance of the parallel plate to be:A commercial capacitor is to be constructed as shown. This particular capacitor is made from two strips of aluminum foil separated by a strip of paraffin-coated paper. Each strip of foil and paper is 7.00 cm wide. The foil is 0.004 00 mm thick, and the paper is 0.025 0 mm thick and has a dielectric constant of 3.70. What length should the strips have if a capacitance of 9.50 x 10-8 F is desired before the capacitor is rolled up? (Adding a second strip of paper and rolling the capacitor would effectively double its capacitance by allowing charge storage on both sides of each strip of foil.)Two plates, each of area 5.30 cm², are 2.59 mm apart in a parallel plate capacitor. The space between the plates is filled with two different dielectric materials. The left half of the capacitor is filled with a material whose dielectric constant K, = 5.50. The right half of the capacitor is filled with a material of unknown dielectric value K2. The capacitance of this device is 7.95 pF. Find the value of K2. Additional Materials еBook e Show My Work (Optional) ?
- Consider the capacitor below, that is not connected to anything. The capacitor has a dielectric between its plates initially. The dielectric is slowly pulled out from between the plates. As that happens, how will the energy stored in the capacitor change? V1+ C1 O It will increase. O It will decrease. O It will stay the same.A parallel-plate capacitor has plates of area 0.11 m2 and a separation of 1.1 cm. A battery charges the plates to a potential difference of 130 V and is then disconnected. A dielectric slab of thickness 3.7 mm and dielectric constant 9.0 is then placed symmetrically between the plates. (a) What is the capacitance before the slab is inserted? (b) What is the capacitance with the slab in place? What is the free charge q (c) before and (d) after the slab is inserted? What is the magnitude of the electric field (e) in the space between the plates and dielectric and (f) in the dielectric itself? (g) With the slab in place, what is the potential difference across the plates? (h) How much external work is involved in inserting the slab? (a) Number i Units (b) Number i Units (c) Number i Units (d) Number Units (e) Number Units (f) Number UnitsA certain substance has a dielectric constant of 2.2 and a dielectric strength of 22 MV/m. If it is used as the dielectric material in a parallel-plate capacitor, what minimum area should the plates of the capacitor have to obtain a capacitance of 10 × 10²µ F and to ensure that the capacitor will be able to withstand a potential difference of 3.4 kV? Number i Units
- First box choices are 4, 3, 6, 1, 2 (V) the second box choices are 1, 8, 3, 1.5, 6 (nJ) and the third box pick from I-VThe dielectric constants shown are κ1 = 1.0, κ2 = 2.0, κ3 = 3.0. The area of each plate is A = 0.20 m2, and the distance between the plates is d = 1.0 mm. The dielectric strength of the entire capacitor is 4.0 MV/m. 3.Find the maximum energy that can be stored on the capacitor. Give an answer in units of mJ. (A) 8.0 (B) 1.0 (C) 6.0 (D) 24 (E) 36A cylindrical capacitor is made of two thin-walled concentric cylinders. The inner cylinder has radius R₂ = 7.5 mm, and the outer one a radius R = 14 mm. The region between the cylinders contains a dielectric with constant =3.6. The common length of the cylinders is L=7.5 m (Assume the cylinders can be treated as ideal infinite cylinders.) Determine the potential energy stored in this capacitor when a potential difference V = 38.8V is applied between the inner and outer cylinders in n.J. ME hp
- A fully charged parallel plate capacitor has a dielectric between its plates. If the dielectric material is removed, the potential difference across the plates increases by 35 %. What is the dielectric constant of the dielectric? Assume that the capacitor is not connected to a source potential after being fully charged.A capacitor is made with plates of area A = 0.255 m2, separated by a distance d = 0.386 mm. Between the plates is a layer of a material with dielectric constant κ = 2.15. What is the capacitance of the capacitor? Your answer should be in nano-farads (nF)An air-filled capacitor is made from two flat parallel plates 1.2 mm apart. The inside area of each plate is 8 cm². (a) What is the capacitance of this set of plates? C F (b) If the region between the plates is filled with a material whose dielectric constant is 6.5, what is the new capacitance? C dielectric air = = F