13. A capacitor is formed of two 1 mm thick parallel plates that are separated by 2 mm. An identical metal plate is now carefully inserted between the two plates so that a space of 0.5 mm is left on either side of the new plate, as shown below. When the metal plate is inserted the capacitance a. decreases. 1 mm b. increases. 2 mm] 1 mm 1 mm

13. A capacitor is formed of two 1 mm thick parallel plates that are separated by 2 mm. An identical metal plate is now carefully inserted between the two plates so that a space of 0.5 mm is left on either side of the new plate, as shown below. When the metal plate is inserted the capacitance a. decreases. 1 mm b. increases. 2 mm] 1 mm 1 mm

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter8: Capacitance

Section: Chapter Questions

Problem 64AP: A capacitor is made from two flat parallel plates placed 0.40 mm apart. When a charge of 0.020C is...

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(i) A battery is attached to several different capacitors connected in parallel. Which of the following statements is true? (a) All capacitors have the same charge, and the equivalent capacitance is greater than the capacitance of any of the capacitors in the group, (b) The capacitor with the largest capacitance carries the smallest charge, (c) The potential difference across each capacitor is the same, and the equivalent capacitance is greater than any of the capacitors in the group. (d) The capacitor with the smallest capacitance carries the largest charge. (e) The potential differences across the capacitors are the same only if the capacitances are the same, (ii) The capacitors are reconnected in series, and the combination is again connected to the battery. From the same choices, choose the one that is true.
A parallel-plate capacitor has capacitance 3.00 F. (a) How much energy is stored in the capacitor if it is connected to a 6.00-V battery? (b) If the battery is disconnected and the distance between the charged plates doubled, what is the energy stored? (c) The battery is subsequently reattached to the capacitor, but the plate separation remains as in part (b). How much energy is stored? (Answer each part in microjoules.)
A nervous physicist worries that the two metal shelves of his wood frame bookcase might obtain a high voltage if charged by static electricity, perhaps produced by friction. (a) What is the capacitance of the empty shelves if they have area 1.00102 m2 and are 0.200 m apart? (b) What is the voltage between them it opposite charges of magnitude 2.00 nC are placed on them? (C) To show that this voltage poses a small hazard, calculate the energy stored.
An anxious physicist worries that the two metal shelves of a wood frame bookcase might obtain a high voltage if charged by static electricity,, perhaps produced by friction, (a) What is the capacitance of the empty shelves if they have area 1.00102m2 and are 0.200 m apart? (b) What is the voltage between them if opposite charges of magnitude 2.00 nC are placed on them? (c) To show that this voltage poses a small hazard, calculate the energy stored, (d) The actual shelves have an area 100 times smaller than these hypothetical shelves. Are his fears justified?
Calculate the equivalent capacitance between points a and b in Figure P26.77. Notice that this system is not a simple series or parallel combination. Suggestion: Assume a potential difference v between [joints a and b. Write expressions for vab in terms of the charges and capacitances for the various possible pathways from a to b and require conservation of charge for those capacitor plates that are connected to each other.
Give a reason why a dielectric material increases capacitance compared with what it would be with air between the plates of a capacitor. How does a dielectric material also allow a greater voltage to be applied to a capacitor? (The dielectric thus increases C and permits a greater V.)
A parallel-plate capacitor has capacitance 3.00 F. (a) How much energy is stored in the capacitor if it is connected to a 6.00-V battery? (b) If the battery is disconnected and the distance between the charged plates doubled, what is the energy stored? (c) The battery is subsequently reattached to the capacitor, but the plate separation remains as in part (b). How much energy is stored? (Answer each part in microjoules.)
Review. A storm cloud and the ground represent the plates of a capacitor. During a storm, the capacitor has a potential difference of 1.00 x 108 V between its plates and a charge of 50.0 C. A lightning strike delivers 1.00% of the energy of the capacitor to a tree on the ground. How much sap in the tree can be boiled away? Model the sap as water initially at 30.0C. Water has a specific heat of 4 186 J/kg C, a boiling point of 100C, and a latent heat of vaporization of 2.26 X 106 J/kg.
True or False? (a) From the definition of capacitance C = Q/V it follows that an uncharged capacitor has a capacitance of zero. (b) As described by the definition of capacitance, the potential difference across an uncharged capacitor is zero.
A 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.
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?
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