Fundamentals of Physics Extended 10e Binder Ready Version + WileyPLUS Registration Card
Fundamentals of Physics Extended 10e Binder Ready Version + WileyPLUS Registration Card
10th Edition
ISBN: 9781118732090
Author: David Halliday
Publisher: Wiley (WileyPLUS Products)
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Chapter 25, Problem 1Q

Figure 25-18 shows plots of charge versus potential difference for three parallel-plate capacitors that have the plate areas and separations given in the table. Which plot goes with which capacitor?

Chapter 25, Problem 1Q, Figure 25-18 shows plots of charge versus potential difference for three parallel-plate capacitors

Figure 25-18 Question 1.

Capacitor Area Separation
1 A d
2 2A d
3 A 2d
Expert Solution & Answer
Check Mark
To determine

To find:

Which plot goes with which capacitor.

Answer to Problem 1Q

Solution:

 Plot a goes with the capacitor 2. The plot b goes with capacitor 1 and plot c goes with capacitor 3.

Explanation of Solution

1) Concept:

Using Eq.25-9, we can find capacitance of each capacitor from the given values of area and plate separation. Then using Eq.25-1, we can compare the capacitance from the slopes of the plots. Then, comparing the predictions about the capacitance yielded from both the equations, we can find out which plot goes with which capacitor.

2) Formulae:

i) From Eq.25-1, the charge q is

q=CV

ii) From Eq.25-9, the capacitance is

C=ε0Ad

3) Given:

i) For capacitor 1, area is A

ii) For capacitor 2, area is 2A

iii) For capacitor 3, area is A

iv) For capacitor 1, separation is d

v) For capacitor 2, separation is d

vi) For capacitor 3, separation is 2d

4) Calculations:

From Eq.25-1, the charge q is

q=CV

where C is the capacitance and V is the potential difference.

Therefore, the capacitance is given by

C=qV=slope.(1)

From Eq.25-9, the capacitance is

C=ε0Ad

where ε0 is the permittivity, A is the area of the plates and d is the separation between the plates.

Let, A=1 and d=1. Putting it in Eq.25-9 we get,

Capacitor 1 has capacitance,

C1=ε011=ε0

Similarly, Capacitor 2 has capacitance,

C2=ε021=2ε0

And Capacitor 3 has capacitance,

C3=ε012=12ε0

From this, we can interpret that capacitance of capacitor 2 has the greatest value and capacitor 1 has the greater capacitance than that of capacitor 3.

From the graph, we can infer that the plot a has the greatest slope. Hence, the capacitance and the slope of plot b is greater than that of plot c. Hence, corresponding capacitance.

Therefore, we can conclude that, Plot a goes with capacitor 2, plot b goes with capacitor 1 and plot c goes with capacitor 3.

Conclusion:

We can predict about the plots between the charge and the voltage corresponding to capacitors having some area and separation between the plates of capacitor from the slope of the graph and the formula for capacitance.

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Chapter 25 Solutions

Fundamentals of Physics Extended 10e Binder Ready Version + WileyPLUS Registration Card

Ch. 25 - You are to connect capacitances C1 and C2, with...Ch. 25 - The two metal objects in Fig. 25-24 have net...Ch. 25 - The capacitor in Fig. 25-25 has a capacitance of...Ch. 25 - SSM A parallel-plate capacitor has circular plates...Ch. 25 - The plates of spherical capacitor have radii 38.0...Ch. 25 - What is the capacitance of a drop that results...Ch. 25 - You have two flat metal plates, each of area...Ch. 25 - If an uncharged parallel-plate capacitor...Ch. 25 - How many 1.00 F capacitors must be connected in...Ch. 25 - Each of the uncharged capacitors in Fig. 25-27 has...Ch. 25 - In Fig. 25-28, find the equivalent capacitance of...Ch. 25 - In Fig. 25-29, find the equivalent capacitance of...Ch. 25 - Two parallel-plate capacitors, 6.0 F each, are...Ch. 25 - SSM ILW A 100 pF capacitor is charged to a...Ch. 25 - GO In Fig. 25-30, the battery has a potential...Ch. 25 - GO In Fig. 25-31, a 20.0 V battery is connected...Ch. 25 - Plot in Fig. 25-32a gives the charge q that can be...Ch. 25 - GO In Fig. 25-29, a potential difference of V =...Ch. 25 - Figure 25-33 shows a circuit section of four...Ch. 25 - GO In Fig. 25-34, the battery has potential...Ch. 25 - Figure 25-35 shows a variable "airgap capacitor...Ch. 25 - SSM WWWIn Fig. 25-36, capacitances are charged C1...Ch. 25 - In Fig. 25-37, V = 10 V, C1 = 10 F, and C2 = C3 =...Ch. 25 - The capacitors in Fig. 25-38 are initially...Ch. 25 - GO Figure 25-39 represents two air-filled...Ch. 25 - GO In Fig. 25-40, two parallel-plate capacitors...Ch. 25 - GO Capacitor 3 in Fig. 25-41a is a variable...Ch. 25 - GO Figure 25-42 shows a 12.0 V battery and four...Ch. 25 - GO Figure 25-43 displays a 12.0 V battery and 3...Ch. 25 - What capacitance is required to store an energy of...Ch. 25 - How much energy is stored in 1.00 m3of air due to...Ch. 25 - SSMA 2.0 F capacitor and a 4.0 F capacitor are...Ch. 25 - A parallel-plate air-filled capacitor having area...Ch. 25 - A charged isolated metal sphere of diameter 10 cm...Ch. 25 - In Fig. 25-28, a potential difference V = 100 V is...Ch. 25 - Assume that a stationary electron is a point of...Ch. 25 - As a safety engineer, you must evaluate the...Ch. 25 - SSM ILW WWW The parallel plates in a capacitor,...Ch. 25 - In Fig. 25-29, a potential difference V = 100 V is...Ch. 25 - Go In Fig. 25-45, C1 = 10.0 F, C2= 20.0 F, and C3...Ch. 25 - An air-filled parallel-plate capacitor has a...Ch. 25 - SSMA coaxial cable used in a transmission line has...Ch. 25 - A parallel-plate air-filled capacitor has a...Ch. 25 - Given a 7.4 pF air-filled capacitor, you are asked...Ch. 25 - You are asked to construct a capacitor having a...Ch. 25 - A certain parallel-plate capacitor is filled with...Ch. 25 - In Fig. 25-46, how much charge is stored on the...Ch. 25 - SSM ILWA certain substance has a dielectric...Ch. 25 - Figure 25-47 shows a parallel-plate capacitor with...Ch. 25 - Figure 25-48 shows a parallel-plate capacitor with...Ch. 25 - Go Figure 25-49 shows a parallel-plate capacitor...Ch. 25 - SSM WWWA parallel-plate capacitor has a...Ch. 25 - For the arrangement of Fig. 25-17, suppose that...Ch. 25 - A parallel-plate capacitor has plates of area 0.12...Ch. 25 - Two parallel plates of area 100 cm2 are given...Ch. 25 - The space between two concentric conducting...Ch. 25 - In Fig. 25-50, the battery potential difference V...Ch. 25 - SSMIn Fig. 25-51, V = 9.0 V, C1 = C2= 30 F, and C3...Ch. 25 - a If C = 50 F in Fig. 25-52, what is the...Ch. 25 - In Fig.25-53, V = 12 V, C1 = C4 = 2.0 F, C2 = 4.0...Ch. 25 - The chocolate crumb mystery. This troy begins with...Ch. 25 - Figure 25-54 shows capacitor 1 C1 = 8.00 F,...Ch. 25 - Two air-filled, parallel-plate capacitors are to...Ch. 25 - Two parallel-plate capacitors, 6.0 F each, are...Ch. 25 - GO In Fig. 25-55, V = 12 V, C1 = C5 = C6 = 6.0 F,...Ch. 25 - SSM In Fig.25-56, the parallel-plate capacitor of...Ch. 25 - A cylindrical capacitor has radii a and b as in...Ch. 25 - A capacitor of capacitance C1 = 6.00 F is...Ch. 25 - Repeat Problem 67 for the same two capacitors but...Ch. 25 - A certain capacitor is charged to a potential...Ch. 25 - Aslab of copper of thickness b = 2.00 mm is thrust...Ch. 25 - Repeat Problem 70, assuming that a potential...Ch. 25 - A potential difference of 300 V is applied to a...Ch. 25 - Figure 25-58 shows a four capacitor arrangement...Ch. 25 - You have two plates of copper, a sheet of mica...Ch. 25 - A capacitor of unknown capacitance Cis charged to...Ch. 25 - A 10 V battery is connected to a series of n...Ch. 25 - SSM In Fig. 25-59, two parallel-plate capacitors A...Ch. 25 - You have many 2.0F capacitors, each capable of...Ch. 25 - A parallel-plate capacitor has charge q and plate...Ch. 25 - A capacitor is charged until its stored energy is...
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