1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Vitek1552 [10]
3 years ago
15

Two fully charged cylindrical capacitors are connected to two identical batteries. The capacitors are identical except that the

radius of the outer plate of capacitor A is four times the radius of the outer plate of capacitor B. Both inner plates have a radius that is half the outer radius of capacitor B.
(a) What is the relative capacitance of each capacitor? Express your answer as a ratio CA/CB.

(b) What is the relative energy stored by each capacitor? Express your answer as a ratio UA/UB.

(c) What is the relative charge stored by each capacitor? Express your answer as a ratio QA/QB.

Physics
1 answer:
Leni [432]3 years ago
8 0

Answer:

Part(a):  The relative capacitance is \dfrac{C_{A}}{C_{B}} = 0.33

Part(b): The relative energy stored is \dfrac{U_{A}}{U_{B}} = 0.33

Part(c): The relative charge stored is \dfrac{Q_{A}}{Q_{B}} = 0.33

Explanation:

We know the capacitance (C) of a capacitor having charge (Q) and subjected to a potential difference of (V) is given by

C = \dfrac{Q}{V}

Also, the energy (U) stored by a capacitor can be written as

U = \dfrac{1}{2}C~V^{2}

Let us assume that the inner radius of the Capacitor B, as shown in the figure, be \textbf{r_{i}^{B}}\bf{r_{i}^{B}}, the outer radius be \bf{r_{o}^{B}}, the inner radius of Capacitor A be \bf{r_{i}^{A}} and the outer radius be \bf{r_{o}^{B}}.

Given in the problem,

&& r_{o}^{B} = 2~r_{B}^{i}\\&& r_{o}^{A} = 4~r_{B}^{i}\\&& and~r_{i}^{B} = 4~r_{o}^{B} = 8~r_{B}^{i}

Now, the capacitance (C) of a cylindrical capacitor is given by,

\bf{C = \dfrac{2~\pi~\epsilon_{0}~L}{ln(\dfrac{r_{o}}{r_{i}})}}

where \epsilon_{o} is the permittivity of the free space, L is the length of the cylindrical capacitor.

Part(a):

The capacitance of capacitor A,

C_{A} = \dfrac{2~\pi~\epsilon_{0}L}{ln(\dfrac{r_{o}^{A}}{r_{i}^{A}})} = \dfrac{2~\pi~\epsilon_{0}L}{ln(\dfrac{8~r_{i}^{B}}{r_{i}^{B}})} = \dfrac{2~\pi~\epsilon_{0}L}{ln(8)}

and the capacitance of capacitor B,

C_{B} = \dfrac{2~\pi~\epsilon_{0}L}{ln(\dfrac{r_{o}^{B}}{r_{i}^{B}})} = \dfrac{2~\pi~\epsilon_{0}L}{ln(\dfrac{2~r_{i}^{B}}{r_{i}^{B}})} = \dfrac{2~\pi~\epsilon_{0}L}{ln(2)}

giving the relative capacitance of each capacitor to be

\dfrac{C_{A}}{C_{B}} = \dfrac{ln(2)}{ln(8)} = \dfrac{ln(2)}{3~\ln(2)} = \dfrac{1}{3} = 0.33

Part(b):

Energy stored by capacitor A,

U_{A} = \dfrac{1}{2}~C_{A}~V^{2}

Energy stored by capacitor B,

U_{B} = \dfrac{1}{2}~C_{B}~V^{2}

giving the relative energy stored by each capacitor to be

\dfrac{U_{A}}{U_{B}} = \dfrac{C_{A}}{C_{B}} = 0.33

Part(c):

The charge stored by capacitor A,

Q_{A} = C_{A}~V

The charge stored by capacitor B,

Q_{B} = C_{B}~V

giving the relative charge stored by each capacitor to be

\dfrac{Q_{A}}{Q_{B}} =  \dfrac{C_{A}}{C_{B}} = 0.33

You might be interested in
A girl and boy pull in opposite directions on a stuffed animal. The girl exerts a force of 3.5 N. The mass of the stuffed animal
Dmitry [639]
The resultant force on the animal = Resultant mass * total acceleration 
F = 0.2 * 2.5 to the right
F = 0.5 to the right.

As, girl exerting a force of 3.5 N & it's not mentioned that she is in right or left, so the force exerting by boy would be either:
3.5-0.5 = 3  OR  3.5+0.5 = 4

If boy exerting a greater force then, answer will be 4 N & if girl exerting a greater force the, answer will be 3 N

Hope this helps!
3 0
3 years ago
Read 2 more answers
Why is it important to understand your strength and weakness<br><br>​
S_A_V [24]

Answer: be a better person

Explanation:

6 0
3 years ago
Read 2 more answers
Science: Please help me with this due in 5 minutes
babunello [35]

Answer: Use less water

only turn on lights when needed

electrical cars

less gas usage

Explanation:

6 0
3 years ago
A convex mirror has a focal length of -10.8 cm. An object is placed 32.7 cm from the mirror's surface. Determine the image dista
KonstantinChe [14]

Answer:

-353.16

Explanation:

4 0
3 years ago
If a client's knees hurt after a one-week walking regimen, which one of the following suggestions is most appropriate?
Flura [38]
A, it's better to take a break to let your body rejuvenate.
5 0
3 years ago
Other questions:
  • Choose the appropriate word choices below that correctly complete the blanks in the following three sentences: At the beginning,
    12·1 answer
  • _ acceleration occurs when an object speeds up.<br> Answer<br> Positive
    10·2 answers
  • An object falls a distance h from rest. If it travels 0.460h in the last 1.00 s, find (a) the time and (b) the height of its fal
    10·2 answers
  • A rock is dropped off a cliff and falls the first half of the distance to the ground in t1 seconds. If it falls the second half
    5·1 answer
  • What is another name for Kepler's Third Law? Select all that apply.
    8·1 answer
  • Two particles with masses m and 3m are moving toward each other along the x axis with the same initial speeds Vi. Particle m is
    11·1 answer
  • How do we know that water dissolves glue?
    10·1 answer
  • A wire carries a current of 0.66 A. This wire makes an angle of 58° with respect to a magnetic field of magnitude 5.50 10-5 T. T
    9·1 answer
  • What energy transformation takes place when you stretch a bungee cord?
    11·1 answer
  • S When two unknown resistors are connected in series with a battery, the battery delivers total power Ps and carries a total cur
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!