Please don't provide handwritten solution ... A parallel-plate capacitor has rectangular plates of length L = 13 cm, width W = 3 cm, and thickness (plate separation) d=3.5 mm (Figure 25-33). Theregion between the plates is filled with a dielectric slab of dielectric constant x = 5.3 which can slide along the length of the capacitor. Initially, the slabcompletely fills the rectangular region, and the capacitor holds a charge of 0.2 Ã‚ÂµC.With the battery DISconnected, how far should the dielectric slab be pulled so that the stored energy is double its initial value?cmWhat is the voltage on the battery?VIWFigure 25-33

Approach to solving the question: To begin with, we calculate the initial capacitance (C_initial) of…

Answered: A parallel-plate capacitor has…

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

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Chapter8: Capacitance

Section: Chapter Questions

Problem 53P: A parallel-plate capacitor has charge of magnitude 9.00F on each plate and capacitance 3.00F when...

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(a) Regarding (lie Earth and a cloud layer 800 m above the Earth as the plates of a capacitor, calculate the capacitance of the Earth-cloud layer system. Assume the cloud layer has an area of 1.00 km2 and the air between the cloud and the ground is pure and dry'. Assume charge builds up on the cloud and on the ground until a uniform electric field of 3.00 106 N/C throughout the space between them makes the air break down and conduct electricity as a lightning bolt, (b) What is the maximum charge the cloud can hold?
What is the maximum charge that can be stored on the 8.00-cm2 plates of an air-filled parallel-plate capacitor beforebreakdown occurs? The dielectric strength of air is 3.00 MV/m.
What If? The two capacitors of Problem 13 (C1 = 5.00 F and C2 = 12.0 F) are now connected in series and to a 9.00-Y battery. Find (a) the equivalent capacitance of the combination. (b) the potential difference across each capacitor, and (c) the charge on each capacitor.
(a) Find the equivalent capacitance between points a and b for the group of capacitors connected as shown in Figure P25.12 (page 686). Take C1 = 5.00 F, C2 = 10.0 F, and C3 = 2.00 F. (b) What charge is stored on C3 if the potential difference between points a and b is 60.0 V? Figure P25.12
An electronics technician wishes to construct a parallel plate capacitor using rutile ( = 100) as the dielectric. The area of the plates is 1.00 cm2. What is the capacitance if the rutile thickness is 1.00 mm? (a) 88.5 pF (b) 177 pF (c) 8.85 F (d) 100 F (e) 35.4 F
A spherical capacitor is formed from two concentric spherical conducting spheres separated by vacuum. Tire inner sphere has radius 12.5 cm and the outer sphere has radius 14.8 cm. A potential difference of 120 V is applied to the capacitor, (a) What is the capacitance of the capacitor? tb) What is the magnitude of the electrical field at r = 12.6 cm, just outside the inner sphere? (c) What is the magnitude of the electrical field at r = 14.7 cm, just inside the outer sphere? (d) For a parallel-plate capacitor the electrical field is uniform in the region between the plates, except near the edges of the plates. Is this also true for a spherical capacitor?
A parallel-plate capacitor with capacitance C0 stores charge of magnitude Q0 on plates of area A0 separated by distance d0. The potential difference across the plates is V0. If the capacitor is attached to a battery and the charge is doubled to 2Q0, what are the ratios (a) Cnew/C0 and (b) Vnew/V0? A second capacitor is identical to the first capacitor except the plate area is doubled to 2A0. If given a charge of Q0, what are the ratios (c) Cnew/C0 and (d) Vnew/V0? A third capacitor is identical to the first capacitor, except the distance between the plates is doubled to 2d0. If the third capacitor is then given a charge of Q0, what are the ratios (e) Cnew/C0 and (f) Vnew/V0?
(i) Rank the following five capacitors from greatest to smallest capacitance, noting any cases of equality, (a) a 20-F capacitor with a 4-V potential difference between its plates (b) a 30-F capacitor with charges of magnitude 90 C on each plate (c) a capacitor with charges of magnitude 80 C on its plates, differing by 2 V in potential. (d) a 10-F capacitor storing energy 125 J (e) a capacitor storing energy 250 J with a 10-V potential difference (ii) Rank the same capacitors in part (i) from largest to smallest according to the potential difference between the plates, (iii) Rank the capacitors in part (i) in the order of the magnitudes of the charges on their plates, (iv) Rank the capacitors in part (i) in the order of the energy they store.
An air-filled capacitor is made from two flat parallel plates 1.0 mm apart. The inside area of each plate is 8.0cm2. (a) What is the capacitance of this set of plates? (b) If the region between the plates is filled with a material whose dielectric constant is 6.0, what is the new capacitance?
The charge density on a disk of radius R = 12.0 cm is given by = ar, with a = 1.40 C/m3 and r measured radially outward from the origin (Fig. P26.45). What is the electric potential at point A, a distance of 40.0 cm above the disk? Hint: You will need to integrate the nonuniform charge density to find the electric potential. You will find a table of integrals helpful for performing the integration.
When a potential difference of 150. V is applied to the plates of an air-filled parallel-plate capacitor, the plates carry a surface charge density of 3.00 1010 C/cm2. What is the spacing between the plates?
An electric potential exists in a region of space such that V = 8x4 2y2 + 9z3 and V is in units of volts, when x, y, and z are in meters. a. Find an expression for the electric field as a function of position. b. What is the electric field at (2.0 m, 4.5 m, 2.0 m)?

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