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In places such as hospital operating rooms or factories for electronic circuit boards, electric sparks must be avoided. A prison standing on a grounded floor and touching nothing else can typically have a body capacitance of 150 pF, in parallel with a foot capacitance of 80.0 pF produced by the dielectric soles of his or her shoes. The person acquires static electric charge from interactions with Ills or her surroundings. The static charge flows to ground through the equivalent resistance of the two shoe soles in parallel with each other. A pair of rubber-soled street shoes can present an equivalent resistance of 5.00 × 103 MΩ. A pair of shoes with special static-dissipative soles can have an equivalent resistance of 1.00 MΩ. Consider the person’s body and shoes as forming an RC circuit with the ground. (a) How long does it take the rubber-soled shoes to reduce a person’s potential from 3.00 × 103 V to 100? (b) How long does it take the static-dissipative shoes to do the same thing?
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Chapter 28 Solutions
Bundle: Physics for Scientists and Engineers, Technology Update, 9th Loose-leaf Version + WebAssign Printed Access Card, Multi-Term
- A spherical capacitor consists of a spherical conducting shell of radius b and charge 2Q that is concentric with a smaller conducting sphere of radius a and charge +Q (Fig. P20.36). (a) Show that its capacitance is C=abke(ba) (b) Show that as b approaches infinity, the capacitance approaches the value a/ke = 40a. Figure P20.36arrow_forwardA parallel-plate capacitor filled with air carries a charge Q. The battery is disconnected, and a slab of material with dielectric constant = 2 is inserted between the plates. Which of the following statements is true? (a) The voltage across the capacitor decreases by a factor of 2. (b) The voltage across the capacitor is doubled. (c) The charge on the plates is doubled. (d) The charge on the plates decreases by a factor of 2. (e) The electric field is doubled.arrow_forwardA parallel-plate capacitor has plates of area A = 7.00 102 m2 separated by distance d = 2.00 104 m. (a) Calculate the capacitance if the space between the plates is filled with air. What is the capacitance if the space is filled half with air and half with a dielectric of constant = 3.70 as in (b) Figure P16.56a, and (c) Figure P16.56b? (Hint: In (b) and (c), one of the capacitors is a parallel combination and the other is a series combination.) Figure P16.56arrow_forward
- A parallel-plate capacitor has square plates that are 8.00 cm on each side and 3.80 mm apart. The space between the plates is completely filled with two square slabs of dielectric, each 8.00 cm on a side and 1.90 mm thick. One slab is Pyrex glass and the other slab is polystyrene. If the potential difference between the plates is 86.0 V, find how much electrical energy can be stored in this capacitor.arrow_forwardA parallel-plate capacitor is charged and then is disconnected from the battery. By what factor does the stored energy change when the plate separation is then doubled? (a) It becomes four times larger. (b) It becomes two times larger. (c) It stays the same. (d) It becomes one-half as large. (e) It becomes one-fourth as large.arrow_forwardA variable air capacitor used in a radio tuning circuit is made of N semicircular plates, each of radius R and positioned a distance d from its neighbors, to which it is electrically connected. As shown in Figure P20.38, a second identical set of plates is enmeshed with the first set. Each plate in the second set is halfway between two plates of the first set. The second set can rotate as a unit. Determine the capacitance as a function of the angle of rotation , where = 0 corresponds to the maximum capacitance. Figure P20.38arrow_forward
- When a Leyden jar is charged by a hand generator (Fig. 27.1, page 828), the work done by the person turning the crank is stored as electric potential energy in the jar. When a capacitor is charged by a battery, where does the electric potential energy come from?arrow_forwardThe dielectric to be used in a parallel-plate capacitor has a dielectric constant of 3.60 and a dielectric strength of 1.60107 V/m. The capacitor has to have a capacitance of 1.25 nF and must be able to withstand a maximum potential difference 5.5 kV. What is the minimum area the plates of the capacitor may have?arrow_forwardA parallel-plate capacitor is connected to a battery. What happens to the stored energy if the plate separation is doubled while the capacitor remains connected to the battery? (a) It remains the same. (b) It is doubled. (c) It decreases by a factor of 2. (d) It decreases by a factor of 4. (e) It increases by a factor of 4.arrow_forward
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