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
pshichka [43]
3 years ago
11

series RC circuit is built with a 15 kΩ resistor and a parallel-plate capacitor with 18-cm-diameter electrodes. A 18 V, 36 kHz s

ource drives a peak current of 0.65 mA through the circuit. Part A What is the spacing between the capacitor plates?
Physics
1 answer:
andre [41]3 years ago
8 0

Answer:

d=1.84\ mm

Explanation:

<u>Capacitance</u>

A two parallel-plate capacitor has a capacitance of

\displaystyle C=\frac{\epsilon_o A}{d}

where

\epsilon_o=8.85\cdot 10^{-12}\ F/m

A = area of the plates = \pi r^2

d = separation of the plates

\displaystyle d=\frac{\epsilon_o A}{C}=\frac{\epsilon_o \pi r^2}{C}

We need to compute C. We'll use the circuit parameters for that. The reactance of a capacitor is given by

\displaystyle X_c=\frac{1}{wC}

where w is the angular frequency

w=2\pi f=2\pi \cdot 36000=226194.67\ rad/s

Solving for C

\displaystyle C=\frac{1}{wX_c}

The reactance can be found knowing the total impedance of the circuit:

Z^2=R^2+X_c^2

Where R is the resistance, R=15 K\Omega=15000\Omega. Solving for Xc

X_c^2=Z^2-R^2

The magnitude of the impedance is computed as the ratio of the rms voltage and rms current

\displaystyle Z=\frac{V}{I}

The rms current is the peak current Ip divided by \sqrt{2}, thus

\displaystyle Z=\frac{\sqrt{2}V}{I_p}

I_p=0.65\ mA/1000=0.00065\ A

Now collect formulas

\displaystyle X_c^2=Z^2-R^2=\left(\frac{\sqrt{2}V}{I_p}\right)^2-R^2

Or, equivalently

\displaystyle X_c=\sqrt{\frac{2V^2}{I_p^2}-R^2}

\displaystyle X_c=\sqrt{\frac{2\cdot 18^2}{0.00065^2}-15000^2}

X_c=36176.34\ \Omega

The capacitance is now

\displaystyle C=\frac{1}{226194.67\cdot 36176.34}=1.22\cdot 10^{-10}\ F

The radius of the plates is

r=18\ cm/2=9 \ cm = 0.09 \ m

The separation between the plates is

\displaystyle d=\frac{8.85\cdot 10^{-12} \cdot \pi\cdot 0.09^2}{1.22\cdot 10^{-10}}

d=0.00184\ m

\boxed{d=1.84\ mm}

You might be interested in
A quantity of 1.922 g of methanol (CH3OH) was burned in a constant-volume calorimeter. Consequently,
White raven [17]
Mass of methanol = 1.922g; Change in temperature = 5.14° C; Heat capacity of the bomb calorimeter + water = 8.69kJ/°C. Number of moles.
3 0
2 years ago
We have two solenoids: solenoid 2 has twice the diameter, half the length, and twice as many turns as solenoid 1. The current in
leva [86]

Answer:

the field at the center of solenoid 2 is 12 times the field at the center of solenoid 1.

Explanation:

Recall that the field inside a solenoid of length L, N turns, and a circulating current I, is given by the formula:

B=\mu_0\, \frac{N}{L} I

Then, if we assign the subindex "1" to the quantities that define the magnetic field (B_1) inside solenoid 1, we have:

B_1=\mu_0\, \frac{N_1}{L_1} I_1

notice that there is no dependence on the diameter of the solenoid for this formula.

Now, if we write a similar formula for solenoid 2, given that it has :

1) half the length of solenoid 1 . Then L_2=L_1/2

2) twice as many turns as solenoid 1. Then N_2=2\,N_1

3) three times the current of solenoid 1. Then I_2=3\,I_1

we obtain:

B_2=\mu_0\, \frac{N_2}{L_2} I_2\\B_2=\mu_0\, \frac{2\,N_1}{L_1/2} 3\,I_1\\B_2=\mu_0\, 12\,\frac{N_1}{L_1} I_1\\B_2=12\,B_1

5 0
3 years ago
If a coin has a mass of 29.34g and drops from a height of 14.7 meters, what is its loss in gravitational potential energy? Show
Serga [27]
U= mgh
U=((29.34/1000)kg)(9.81 \frac{m}{s^{2} } )(14.7m)=4.321J

do not forget to change grams to kilograms and if it were in centimeters convert them to meters.
7 0
3 years ago
The wave length of violet light rounded to the nearest nanometer is a __ nm
nataly862011 [7]
Wavelength= speed / frequency 

so.....3× 10^8 / 7.26×10^14
= .413× 10^(-6)

in scientific notation= 4.13×10^(-7) 

in nanometer = 413 nm
6 0
3 years ago
Consider the same 70kg/686N student on the surface on another planet from the table above: Jupiter. Tompared to the gravitationa
Yuliya22 [10]

Answer:

Dont mind me

Explanation:

6 0
3 years ago
Other questions:
  • How to win friends and influence people
    12·1 answer
  • I need help, please help an object starts from rest at time t=0 and moves in the with constant acceleration. The object travels
    9·1 answer
  • Match the following rocks with the correct type.
    7·2 answers
  • Which feature forms most of the ocean floor. describe it in detail
    8·1 answer
  • According to Newton’s First Law of Motion, if a ball is rolled in a straight line in an open field, what will happen to the ball
    5·1 answer
  • I have a set of calipers that can measure thickness of a few inches with an uncertainty of ±0.005 inches. I measure the thicknes
    10·1 answer
  • How does energy release from the sun reach Earth? How does the sun's energy interact with Earth's atmosphere and hydrosphere?
    13·2 answers
  • PLZ help 10 points!!! space question!
    7·1 answer
  • PLS HELP ASAP<br><br> Assignment due in 30 min and a LOT more questions
    5·2 answers
  • A 64.1 kg runner has a speed of 3.10 m/s at one instant during a long-distance event.(a) What is the runner's kinetic energy at
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!