Principles of Physics

David Halliday , Robert Resnick , Jearl Walker

Chapter 25

Capacitance - all with Video Answers

Educators

Chapter Questions

Problem 1

In Fig. $25-18, \quad C_{1}=10.0 \mu \mathrm{F}$, $C_{2}=5.0 \mu \mathrm{F}$, and $C_{3}=4.0 \mu \mathrm{F} .$ What is the change in their equivalent capacitance if (a) capacitors 1 and 2 are interchanged and (separately) (b) capacitors 1 and 3 are interchanged?

Sunita Kumari

Sunita Kumari

Numerade Educator

Problem 2

In Fig. 25-18, a potential difference $V=75.0 \mathrm{~V}$ is applied across a capacitor arrangement with capacitances $C_{1}=10.0 \mu \mathrm{F}, C_{2}=5.00 \mu \mathrm{F}$, and $C_{3}=15.0 \mu \mathrm{F}$. What are (a) charge $q_{3}$, (b) potential difference $V_{3}$, and (c) stored energy $U_{3}$ for capacitor 3, (d) $q_{1}$, (e) $V_{1}$, and (f) $U_{1}$ for capacitor 1 , and (g) $q_{2}$, (h) $V_{2}$, and (i) $U_{2}$ for capacitor 2?

Sunita Kumari

Numerade Educator

Problem 3

In Fig. 25-18, a potential difference of $V=65.0 \mathrm{~V}$ is applied across a capacitor arrangement with capacitances $C_{1}=10.0 \mu \mathrm{F}$, $C_{2}=5.00 \mu \mathrm{F}$, and $C_{3}=4.00 \mu \mathrm{F}$. If capacitor 3 undergoes electrical breakdown so that it becomes equivalent to conducting wire, then for capacitor 1 what are the increases in (a) charge, (b) potential difference, and (c) stored energy?

Sunita Kumari

Numerade Educator

Problem 4

In Fig. 25-19, find the equivalent capacitance of the combination. Assume that $C_{1}$ is $10.0 \mu \mathrm{F}, C_{2}$ is $8.00$ $\mu \mathrm{F}$, and $C_{3}$ is $4.00 \mu \mathrm{F}$.

Sunita Kumari

Numerade Educator

Problem 5

What capacitance is required to store an energy of $10 \mathrm{~kW} \cdot \mathrm{h}$ at a potential difference of $1700 \mathrm{~V}$ ?

Sunita Kumari

Numerade Educator

Problem 6

In Fig. $25-19$, a potential difference $V=100 \mathrm{~V}$ is applied across a capacitor arrangement with capacitances $C_{1}=10.0 \mu \mathrm{F}, C_{2}=5.00 \mu \mathrm{F}$, and $C_{3}=2.00 \mu \mathrm{F}$. What are (a) charge $q_{3}$, (b) potential difference $V_{3}$, and (c) stored energy $U_{3}$ for capacitor 3, (d) $q_{1}$, (e) $V_{1}$, and (f) $U_{1}$ for capacitor 1, and $(\mathrm{g}) q_{2},(\mathrm{~h}) V_{2}$, and $(\mathrm{i}) U_{2}$ for capacitor $2 ?$

Sunita Kumari

Numerade Educator

Problem 7

A parallel-plate capacitor has plates of area $0.080 \mathrm{~m}^{2}$ and a separation of $1.2 \mathrm{~cm}$. A battery charges the plates to a potential difference of $120 \mathrm{~V}$ and is then disconnected. A dielectric slab of thickness $4.0 \mathrm{~mm}$ and dielectric constant $4.8$ 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?

Sunita Kumari

Numerade Educator

Problem 8

Figure $25-20$ displays a $16.0 \mathrm{~V}$ battery and 3 uncharged capacitors of capacitances $C_{1}=4.00 \mu \mathrm{F}$, $C_{2}=6.00 \mu \mathrm{F}$, and $C_{3}=3.00 \mu \mathrm{F}$. The switch is thrown to the left side until capacitor 1 is fully charged. Then the switch is thrown to the right. What is the final charge on (a) capacitor 1 , (b) capacitor 2, and $(\mathrm{c})$ capacitor $3 ?$

Sunita Kumari

Numerade Educator

Problem 9

In Fig. 25-21, the battery has potential difference $V=14.0 \mathrm{~V}$, $C_{2}=3.0 \mu \mathrm{F}, C_{4}=4.0 \mu \mathrm{F}$, and all the capacitors are initially uncharged. When switch $\mathrm{S}$ is closed, a total charge of $12 \mu \mathrm{C}$ passes through point $a$ and a total charge of $8.0 \mu \mathrm{C}$ passes through point $b .$ What are (a) $C_{1}$ and (b) $C_{3}$ ?

Sunita Kumari

Numerade Educator

Problem 10

A parallel-plate air-filled capacitor having area $40 \mathrm{~cm}^{2}$ and plate spacing $1.0 \mathrm{~mm}$ is charged to a potential difference of $500 \mathrm{~V}$. Find (a) the capacitance, (b) the magnitude of the charge on each plate, (c) the stored energy, (d) the electric field between the plates, and (e) the energy density between the plates.

Sunita Kumari

Numerade Educator

Problem 11

A dielectric material is to fill the space in a capacitor. Initially, with only air in place, the capacitance is $8.0 \mathrm{pF}$. With the dielectric material in place, the capacitor should store $3.2 \mu \mathrm{J}$ at a maximum potential difference of $350.8 \mathrm{~V}$. (a) What dielectric constant is required? (b) Of the materials in Table $25-1$, which material should be used?

Sunita Kumari

Numerade Educator

Problem 12

An air-filled parallel-plate capacitor has a capacitance of $2.1 \mathrm{pF}$. The separation of the plates is doubled, and wax is inserted between them. The new capacitance is $2.6 \mathrm{pF}$. Find the dielectric constant of the wax.

Sunita Kumari

Numerade Educator

Problem 13

A $2.0 \mu \mathrm{F}$ capacitor and a $4.0 \mu \mathrm{F}$ capacitor are connected in parallel across a $300 \mathrm{~V}$ potential difference. (a) What is the total energy stored by them? (b) They are next connected in series across that potential difference. What is the ratio of the total energy stored by them in the parallel arrangement to that in the series arrangement?

Sunita Kumari

Numerade Educator

Problem 14

In Fig. $25-22$, how much charge is stored on the parallel-plate capacitors by the $10.0 \mathrm{~V}$ battery? One is filled with air, and the other is filled with a dielectric for which $\kappa=3.00$; both capacitors have a plate area of $5.00 \times 10^{-3} \mathrm{~m}^{2}$ and a plate separation of $2.00 \mathrm{~mm}$.

Sunita Kumari

Numerade Educator

Problem 15

Assume that a stationary electron is a point of charge. What is the energy density $u$ of its electric field at radial distances (a) $r=1.00 \mathrm{~mm}$, (b) $r=1.00 \mu \mathrm{m}$, (c) $r=1.00 \mathrm{~nm}$, (d) $r=1.00 \mathrm{pm}$, and (e) $r=1.00 \mathrm{fm}$ ? (f) What is $u$ in the limit as $r \rightarrow 0$ ?

Sunita Kumari

Numerade Educator

Problem 16

You are asked to construct a capacitor having a capacitance near $1 \mathrm{nF}$ and a breakdown potential in excess of $10000 \mathrm{~V}$. You think of using the sides of a tall Pyrex drinking glass as a dielectric, lining the inside and outside curved surfaces with aluminum foil to act as the plates. The glass is $10 \mathrm{~cm}$ tall with an inner radius of $3.6 \mathrm{~cm}$ and an outer radius of $3.8 \mathrm{~cm}$. What are the (a) capacitance and (b) breakdown potential of this capacitor?

Sunita Kumari

Numerade Educator

Problem 17

The parallel plates in a capacitor, with a plate area of $8.50 \mathrm{~cm}^{2}$ and an air-filled separation of $8.00 \mathrm{~mm}$, are charged by a $16.0 \mathrm{~V}$ battery. They are then disconnected from the battery and pushed together (without discharge) to a separation of $3.00 \mathrm{~mm}$. Neglecting fringing, find (a) the potential difference between the plates, (b) the initial stored energy, (c) the final stored energy, and (d) the (negative) work in pushing them together.

Sunita Kumari

Numerade Educator

Problem 18

Figure 25-23 shows a parallel plate capacitor with a plate area $A=$ $5.56 \mathrm{~cm}^{2}$ and separation $d=5.56$ $\mathrm{mm}$. The left half of the gap is filled with material of dielectric constant $\kappa_{1}=7.00$; the right half is filled with material of dielectric constant $\kappa_{2}=10.0 .$ What is the capacitance?

Sunita Kumari

Numerade Educator

Problem 19

In Fig. 25-24, $C_{1}=10.0 \mu \mathrm{F}$, $C_{2}=20.0 \mu \mathrm{F}$, and $C_{3}=5.00$ $\mu \mathrm{F}$. If no capacitor can withstand a potential difference of more than $100 \mathrm{~V}$ without failure, what are (a) the magnitude of the maximum potential difference that can exist between points $A$ and $B$ and (b) the maximum energy that can be stored in the three-capacitor arrangement?

Sunita Kumari

Numerade Educator

Problem 20

As a safety engineer, you must evaluate the practice of storing flammable conducting liquids in nonconducting containers. The company supplying a certain liquid has been using a squat, cylindrical plastic container of radius $r=0.20 \mathrm{~m}$ and filling it to height $h=10 \mathrm{~cm}$, which is not the container's full interior height (Fig. 25-25). Your investigation reveals that during handling at the company, the exterior surface of the container commonly acquires a negative charge density of magnitude $2.0 \mu \mathrm{C} / \mathrm{m}^{2}$ (approximately uniform). Because the liquid is a conducting material, the charge on the container induces charge separation within the liquid. (a) How much negative charge is induced in the center of the liquid's bulk? (b) Assume the capacitance of the central portion of the liquid relative to ground is $50 \mathrm{pF}$. What is the potential energy associated with the negative charge in that effective capacitor? (c) If a spark occurs between the ground and the central portion of the liquid (through the venting port), the potential energy can be fed into the spark. The minimum spark energy needed to ignite the liquid is $10 \mathrm{~mJ}$. In this situation, can a spark ignite the liquid?

Keshav Singh

Numerade Educator

Problem 21

A coaxial cable used in a transmission line has an inner radius of $0.10 \mathrm{~mm}$ and an outer radius of $0.40 \mathrm{~mm}$. Calculate the capacitance per meter for the cable. Assume that the space between the conductors is filled with epoxy resin with dielectric constant $3.6$.

Sunita Kumari

Numerade Educator

Problem 22

Figure 25-26 shows a parallel-plate capacitor of plate area $A=12.5 \mathrm{~cm}^{2}$ and plate separation $2 d=7.12 \mathrm{~mm}$. The left half of the gap is filled with material of dielectric constant $\kappa_{1}=21.0$; the top of the right half is filled with material of dielectric constant $\kappa_{2}=42.0 ;$ the bottom of the right half is filled with material of dielectric constant $\kappa_{3}=58.0$. What is the capacitance?

Sunita Kumari

Numerade Educator

Problem 23

A parallel-plate capacitor has square plates with edge length $8.20 \mathrm{~cm}$ and $1.30 \mathrm{~mm}$ separation. (a) Calculate the capacitance. (b) Find the charge for a potential difference of $120 \mathrm{~V}$.

Sunita Kumari

Numerade Educator

Problem 24

In Fig. 25-27, the battery has a potential difference of $V=12.0 \mathrm{~V}$ and the five capacitors each have a capacitance of $10.0 \mu \mathrm{F}$. What is the charge on (a) capacitor 1 and (b) capacitor $2 ?$

Sunita Kumari

Numerade Educator

Problem 25

A certain parallel-plate capacitor is filled with a dielectric for which $\kappa=2.4$. The area of each plate is $0.017 \mathrm{~m}^{2}$, and the plates are separated by $2.0 \mathrm{~mm}$. The capacitor will fail (short out and burn up) if the electric field between the plates exceeds $200 \mathrm{kN} / \mathrm{C}$. What is the maximum energy that can be stored in the capacitor?

Sunita Kumari

Numerade Educator

Problem 26

How much energy is stored in $1.00 \mathrm{~m}^{3}$ of air due to the "fair weather" electric field of magnitude $120 \mathrm{~V} / \mathrm{m}$ ?

Sunita Kumari

Numerade Educator

Problem 27

A parallel-plate capacitor has a capacitance of $100 \mathrm{pF}$, a plate area of $80 \mathrm{~cm}^{2}$, and a mica dielectric $(\kappa=5.4)$ completely filling the space between the plates. At $85 \mathrm{~V}$ potential difference, calculate (a) the electric field magnitude $E$ in the mica, (b) the magnitude of the free charge on the plates, and (c) the magnitude of the induced surface charge on the mica.

Sunita Kumari

Numerade Educator

Problem 28

A parallel-plate air-filled capacitor has a capacitance of $50 \mathrm{pF}$. (a) If each of its plates has an area of $0.30 \mathrm{~m}^{2}$, what is the separation? (b) If the region between the plates is now filled with material having $\kappa=5.6$, what is the capacitance?

Sunita Kumari

Numerade Educator

Problem 29

Each of the uncharged capacitors in Fig. $25-28$ has a capacitance of $25.0 \mu \mathrm{F}$. A potential difference of $V=750 \mathrm{~V}$ is established when the switch is closed. How many coulombs of charge then pass through meter A?

Sunita Kumari

Numerade Educator

Problem 30

Figure 25-29 shows a variable "air gap" capacitor for manual tuning. Alternate plates are connected together; one group of plates is fixed in position, and the other group is capable of rotation. Consider a capacitor of $n=8$ plates of alternating polarity, each plate having area $A=1.50 \mathrm{~cm}^{2}$ and separated from adjacent plates by distance $d=3.40 \mathrm{~mm}$. What is the maximum capacitance of the device?

Sunita Kumari

Numerade Educator

Problem 31

Figure 25-30 shows a parallel-plate capacitor with a plate area $A=7.89 \mathrm{~cm}^{2}$ and plate separation $d=4.62 \mathrm{~mm}$. The top half of the gap is filled with material of dielectric constant $\kappa_{1}=11.0$; the bottom half is filled with material of dielectric constant $\kappa_{2}=4.0$. What is the capacitance?

Sunita Kumari

Numerade Educator

Problem 32

The capacitor in Fig. $25-31$ has a capacitance of $30 \mu \mathrm{F}$ and is initially uncharged. The battery provides a potential difference of $120 \mathrm{~V}$. After switch $S$ is closed, how much charge will pass through it?

Sunita Kumari

Numerade Educator

Problem 33

If an uncharged parallel-plate capacitor (capacitance $C$ ) is connected to a battery, one plate becomes negatively charged as electrons move to the plate face (area $A$ ). In Fig. $25-32$, the depth $d$ from which the electrons come in the plate in a particular capacitor is plotted against a range of values for the potential difference $V$ of the battery. The density of conduction electrons in the copper plates is $8.49 \times 10^{28}$ electrons $/ \mathrm{m}^{3}$. The vertical scale is set by $d_{s}=2.00 \mathrm{pm}$, and the horizontal scale is set by $V_{s}=20.0 \mathrm{~V}$. What is the ratio $C / A$ ?

Sunita Kumari

Numerade Educator

Problem 34

Two parallel-plate capacitors, $8.0 \mu \mathrm{F}$ each, are connected in parallel to a $10 \mathrm{~V}$ battery. One of the capacitors is then squeezed so that its plate separation is $50.0 \%$ of its initial value. Because of the squeezing, (a) how much additional charge is transferred to the capacitors by the battery and (b) what is the increase in the total charge stored on the capacitors?

Sunita Kumari

Numerade Educator

Problem 35

In Fig. 25-33, a $20.0 \mathrm{~V}$ battery is connected across capacitors of capacitances $C_{1}=C_{6}=6.00 \mu \mathrm{F}$ and $C_{3}=C_{5}=2.00 C_{2}=2.00 C_{4}=$ $4.00 \mu \mathrm{F}$. What are (a) the equivalent capacitance $C_{\mathrm{eq}}$ of the capacitors and (b) the charge stored by $C_{\text {eq }}$ ? What are (c) $V_{1}$ and (d) $q_{1}$ of capacitor 1, (e) $V_{2}$ and (f) $q_{2}$ of capacitor 2, and (g) $V_{3}$ and (h) $q_{3}$ of capacitor 3 ?

Sunita Kumari

Numerade Educator

Problem 36

Figure $25-34$ represents two airfilled cylindrical capacitors connected in series across a battery with potential $V=10 \mathrm{~V}$. Capacitor 1 has an inner plate radius of $3.00 \mathrm{~mm}$, an outer plate radius of $1.5 \mathrm{~cm}$, and a length of $5.0 \mathrm{~cm}$. Capacitor 2 has an inner plate radius of $2.5 \mathrm{~mm}$, an outer plate radius of $1.0 \mathrm{~cm}$, and a length of $9.0 \mathrm{~cm}$. The outer plate of capacitor 2 is a conducting organic membrane that can be stretched, and the capacitor can be inflated to increase the plate separation. If the outer plate radius is increased to $2.5 \mathrm{~cm}$ by inflation, (a) how many electrons move through point $P$ and (b) do they move toward or away from the batterv?

Sunita Kumari

Numerade Educator

Problem 37

A certain substance has a dielectric constant of $5.6$ and a dielectric strength of $18 \mathrm{MV} / \mathrm{m}$. 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 $3.9 \times 10^{-2} \mu \mathrm{F}$ and to ensure that the capacitor will be able to withstand a potential difference of $4.0 \mathrm{kV}$ ?

Sunita Kumari

Numerade Educator

Problem 38

For the arrangement of Fig. 25-17, suppose that the battery remains connected while the dielectric slab is being introduced. Calculate (a) the capacitance, (b) the charge on the capacitor plates, (c) the electric field in the gap, and (d) the electric field in the slab, after the slab is in place.

Ze-Han Lee

Numerade Educator

Problem 39

In Fig. $25-35$, the capacitances are $C_{1}=1.0 \mu \mathrm{F}$ and $C_{2}=3.0 \mu \mathrm{F}$, and both capacitors are charged to a potential difference of $V=200 \mathrm{~V}$ but with opposite polarity as shown. Switches $S_{1}$ and $S_{2}$ are now closed. (a) What is now the potential difference between points $a$ and $b$ ? What now is the charge on capacitor (b) 1 and (c) 2 ?

Sunita Kumari

Numerade Educator

Problem 40

Capacitor 3 in Fig. $25-36 a$ is a variable capacitor (its capacitance $C_{3}$ can be varied). Figure $25-36 b$ gives the electric potential $V_{1}$ across capacitor 1 versus $C_{3}$. The horizontal scale is set by $C_{3 s}=12.0 \mu \mathrm{F}$. Electric potential $V_{1}$ approaches an asymptote of $8.0 \mathrm{~V}$ as $C_{3} \rightarrow \infty$. What are (a) the electric potential $V$ across the battery, (b) $C_{1}$, and (c) $C_{2} ?$

Sunita Kumari

Numerade Educator

Problem 41

The capacitors in Fig. 25-37 are initially uncharged. The capacitances are $C_{1}=4.0 \mu \mathrm{F}, \quad C_{2}=8.0 \mu \mathrm{F}, \quad$ and $C_{3}=12 \mu \mathrm{F}$, and the battery's potential difference is $V=6.0 \mathrm{~V}$. When switch $\mathrm{S}$ is closed, how many electrons travel through (a) point $a$, (b) point $b$, (c) point $c$, and (d) point $d$ ? In the figure, do the electrons travel up or down through (e) point $b$ and (f) point $c$ ?

Sunita Kumari

Numerade Educator

Problem 42

Figure $25-38$ shows a circuit section of four air-filled capacitors that is connected to a larger circuit. The graph below the section shows the electric potential $V(x)$ as a function of position $x$ along the lower part of the section, through capacitor 4. Similarly, the graph above the section shows the electric potential $V(x)$ as a function of position $x$ along the upper part of the section, through capacitors 1,2 , and 3 . Capacitor 3 has a capacitance of $1.60 \mu \mathrm{F}$. What are the capacitances of (a) capacitor 1 and (b) capacitor 2 ?

Ze-Han Lee

Numerade Educator

Problem 43

A charged isolated metal sphere of diameter $15 \mathrm{~cm}$ has a potential of $6500 \mathrm{~V}$ relative to $V=0$ at infinity. (a) Calculate the energy density in the electric field near the surface of the sphere. (b) If the diameter is decreased, does the energy density near the surface increase, decrease, or remain the same?

Sunita Kumari

Numerade Educator

Problem 44

Two parallel plates of area $100 \mathrm{~cm}^{2}$ are given charges of equal magnitudes $8.4 \times 10^{-7} \mathrm{C}$ but opposite signs. The electric field within the dielectric material filling the space between the plates is $1.4 \times 10^{6} \mathrm{~V} / \mathrm{m}$. (a) Calculate the dielectric constant of the material. (b) Determine the magnitude of the charge induced on each dielectric surface.

Sunita Kumari

Numerade Educator

Problem 45

What is the capacitance of a drop that results when two mercury spheres, each of radius $R=3.00 \mathrm{~mm}$, merge?

Sunita Kumari

Numerade Educator

Problem 46

Plot 1 in Fig. 25-39a gives the charge $q$ that can be stored on capacitor 1 versus the electric potential $V$ set up across it. The vertical scale is set by $q_{s}=16.0 \mu \mathrm{C}$, and the horizontal scale is set by $V_{s}=2.0 \mathrm{~V}$. Plots 2 and 3 are similar plots for capacitors 2 and 3 , respectively. Figure $25-39 \mathrm{~b}$ shows a circuit with those three capacitors and a $10.0 \mathrm{~V}$ battery. What is the charge stored on capacitor 2 in that circuit?

Sunita Kumari

Numerade Educator

Problem 47

Figure $25-40$ shows a $24.0 \mathrm{~V}$ battery and four uncharged capacitors of capacitances $C_{1}=1.00 \mu \mathrm{F}$, $C_{2}=2.00 \mu \mathrm{F}, C_{3}=3.00 \mu \mathrm{F}$, and $C_{4}=4.00 \mu \mathrm{F}$. If only switch $\mathrm{S}_{1}$ is closed, what is the charge on (a) capacitor 1, (b) capacitor 2, (c) capacitor 3 , and (d) capacitor 4 ? If both switches are closed, what is the charge on (e) capacitor 1, (f) capacitor 2, (g) capacitor 3, and (h) capacitor 4 ?

Sunita Kumari

Numerade Educator

Problem 48

How many $12.5 \mu \mathrm{F}$ capacitors must be connected in parallel to store a charge of $33.0 \mathrm{mC}$ with a potential of $110 \mathrm{~V}$ across the capacitors?

Sunita Kumari

Numerade Educator

Problem 49

The space between two concentric conducting spherical shells of radii $b=1.70 \mathrm{~cm}$ and $a=1.20 \mathrm{~cm}$ is filled with a substance of dielectric constant $\kappa=6.91$. A potential difference $V=73.0 \mathrm{~V}$ is applied across the inner and outer shells. Determine (a) the capacitance of the device, (b) the free charge $q$ on the inner shell, and (c) the charge $q^{\prime}$ induced along the surface of the inner shell.

Sunita Kumari

Numerade Educator

Problem 50

You have two flat metal plates, each of area $1.00 \mathrm{~m}^{2}$, with which to construct a parallel-plate capacitor. (a) If the capacitance of the device is to be $2.00 \mathrm{~F}$, what must be the separation between the plates? (b) Could this capacitor actually be constructed?

Sunita Kumari

Numerade Educator

Problem 51

The two metal objects in Fig. $25-41$ have net charges of $+70 \mathrm{pC}$ and $-70 \mathrm{pC}$, which result in a $35 \mathrm{~V}$ potential difference between them. (a) What is the capacitance of the system? (b) If the charges are changed to $+200 \mathrm{pC}$ and $-200 \mathrm{pC}$, what does the capacitance become? (c) What does the potential difference become?

Sunita Kumari

Numerade Educator

Problem 52

In Fig. 25-42, $V=12 \mathrm{~V}, C_{1}=10 \mu \mathrm{F}$, and $C_{2}=C_{3}=20 \mu \mathrm{F}$. Switch $\mathrm{S}$ is first thrown to the left side until capacitor 1 reaches equilibrium. Then the switch is thrown to the right. When equilibrium is again reached, how much charge is on capacitor 1 ?

Sunita Kumari

Numerade Educator

Problem 53

A $100 \mathrm{pF}$ capacitor is charged to a potential difference of $80.0 \mathrm{~V}$, and the charging battery is disconnected. The capacitor is then connected in parallel with a second (initially uncharged) capacitor. If the potential difference across the first capacitor drops to $35.0 \mathrm{~V}$, what is the capacitance of this second capacitor?

Sunita Kumari

Numerade Educator

Problem 54

The plates of a spherical capacitor have radii $37.0 \mathrm{~mm}$ and $40.0 \mathrm{~mm}$. (a) Calculate the capacitance. (b) What must be the plate area of a parallel-plate capacitor with the same plate separation and capacitance?

Sunita Kumari

Numerade Educator

Problem 55

In Fig. 25-43, two parallel-plate capacitors (with air between the plates) are connected to a battery. Capacitor 1 has a plate area of $1.5 \mathrm{~cm}^{2}$ and an electric field (between its plates) of magnitude $3500 \mathrm{~V} / \mathrm{m}$. Capacitor 2 has a plate area of $0.70 \mathrm{~cm}^{2}$ and an electric field of magnitude $1500 \mathrm{~V} / \mathrm{m}$. (a) What is the total charge on the two capacitors? (b) If the first plate area is cut in half, does the total charge increase, decrease, or remain the same?

Sunita Kumari

Numerade Educator