58. ★★ A parallel-plate capacitor has plates of area A and separation d. Two different dielectrics (K₁, K₂) are inserted (Figure 22-27), each filling half the space. Derive an expression for the capacitance. (Hint: Treat the setup as two capacitors in parallel.) K₁ K₂

58. ★★ A parallel-plate capacitor has plates of area A and separation d. Two different dielectrics (K₁, K₂) are inserted (Figure 22-27), each filling half the space. Derive an expression for the capacitance. (Hint: Treat the setup as two capacitors in parallel.) K₁ K₂

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

A parallel-plate capacitor of capacitance C0 = ε0A0/d0 , is connected to a battery. When the capacitor is fully charged, it is disconnected from the battery (initial state). We push the plates closer together, until d = d0/2 (final state). a) How does the energy stored in the capacitor change (increase or decrease)? Justify your answer. b) Calculate Ufinal / Uinitial , in terms of the parameters defined in the problem.
Two capacitors are identical, except that one is empty and the other is filled with a dielectric (k = 3.4). The empty capacitor is connected to a 13-V battery. What must be %3D the potential difference across the plates of the capacitor filled with a dielectric so that it stores the same amount of electrical energy as the empty capacitor? V2 = i
A potential difference AV is applied across the combination of capacitors shown in the figure, where C1=3.0 µF and C2=6.0 µF. Which statement(s) in what follows is/are correct? AV I: The energy stored in C1 is greater than that stored in C. II: The voltage across C1 would be higher if C1 had a dielectric material K1 between its plates. III: The equivalent capacitance is increased if two dielectrics (of Kį and K2) are, respectively, inserted in C1 and C2. O I and II O I and III O Il and II O II only. O None of the options above.
1. An air-filled capacitor is made from two flat parallel plates 1.5 mm apart. The inside area of each plate is 7.9 cm². (a) What is the capacitance of this set of plates? F Cair = (b) If the region between the plates is filled with a material whose dielectric constant is 6, what is the new capacitance? C dielectric = F
100 There is a system with four capacitors connected, as shown in Figure P25.10. (a) Calculate the equivalent capacity between points a and b. (b) Find the charge amount of each capacitor when the potential difference AV between points a and bis 15.0 V. 11 (13). Find the equivalent capacitance a 15.0μF 3.00 μF 120.0 με 16: HH 6.00 με Figure P25.10
) A stegosaurus works to provide emergency roadside assistance for stranded travelers. Much of her job involves jump starting car batteries. For convenience, she often covers the bony plates on her back with metal to create parallel plate capacitors - these provide an extra boost to the battery. 1. (a) are triangle shaped with base 0.40 m and height 0.40 m. Each set of 2 plates is a distance d = 0.1m apart. What is the capacitance of a single set of 2 plates? Assume the stegasaurus has 17 sets of 2 plates on her back. All plates (b) parallel, what is the total capacitance of the stegosaurus? Assuming that the plates are wired so that all 17 sets of plates are in
A capacitor is constructed out of two foil wrappers that have a length of 8.7 cm and width of 2.1 cm, and the plates (wrappers) are spaced 7 μm apart. If the capacitor is filled with a dielectric that has a constant of 120, what is the capacitance? (in F) a. 6.69×10-8 F b. 3.61×10-6 F c. 2.31×10-9 F d. 1.92×10-11 F e. 2.77×10-7 F
You have a capacitor made of two sheets of foil of area 2.7 cm2 separated by a distance 0.5 mm. a) what is the capacitance (in pF(10-12F)) of this capacitor? b) what is the voltage across the capacitor if 7 x 10-12 C is stored? c) how much energy is stored in the capacitor?
25. -3 points SercP11 16.8.P056. My Notes Ask Your Teacher A parallel plate capacitor has plates of area A-6.50 x 10-2 m2 separated by distance d-147x 10-4 m. The permitti ity of ree space ise 885 x 10-12- N . HINT (a) Calculate the capacitance (in F) if the space between the plates is filled with air What is the capacitance (in F) if the space is filled half with air and half with a dielectric of constant K-2.70 as in figure (a), and figure (b)? (Hint: One of the capacitors is a parallel combination and the other is a series combination.) (b) figure (a) (c) figure (b)
1. Two capacitors with 2.0 F and 3.0 F capacitance, respectively, are connected in parallel. The combination is connected to a 100 V line. Find the (a) total capacitance, (b) charge stored in each capacitor, and (c) potential difference across each capacitor. 2. parallel plate capacitor consists of two rectangular plates, each with an area of 4.5 cm2 and are separated from each other by a 2.00 mm thick dielectric with a dielectric constant of 5.26. The capacitor is connected to a 12.0 V battery. How much energy is stored in the capacitor?
2) The capacitances are C₁ = 1.0 mF and C₂ = 3.0 mF, and both capacitors are charged to a potential difference of V = 100 V but with opposite polarity as shown. Switches S₁ and S₂ are now closed. a) What is now the potential difference between points a and b? b) What now is the charge on each capacitor? G a Sq
*3 Problem 1: Consider a parallel-plate capacitor made up of two conducting plates with dimensions 39 mm × 32 mm. Part (a) If the separation between the plates is 1.1 mm, what is the capacitance, in pF, between them? C = 1.00 7 (789 HOME EM 4 5 6 sin() cos( tan() cotan() asin() acos() atan() acotan() sinh() cosh() tanh() cotanh() Degrees O Radians /* 1 2 3 0 VO BACKSPACE DEL Part (b) If there is 0.59 nC of charged stored on the positive plate, what is the potential, in volts, across the capacitor? V= E' = sin()) cotan() atan() cosh() cos() tan() asin() acos() acotan() sinh() 4 5 6 12 3 0 NO BACKSPACE DEL CLEAR + - END tanh() cotanh() Degrees O Radians Part (c) What is the magnitude of the electric field, in newtons per coulomb, inside this capacitor? E=| → sin() cos() cotan() asin() atan() acotan cosh() END CLEAR πι() 7 8 9 EL acos() sinh() tan() T () 7 ETAAL 4 / tanh() cotanh() ⒸDegrees O Radians tan() T() 7 89 HOME sin()) cos() cotan() asin() E^4 acos() sinh() 5 6 1 2 3 cosh() atan()…