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
An automobile is traveling away from Jill and towards Jack. The horn is honking, producing a sound wave.
wlad13 [49]

Answer:

a. The sound will travel at the speed to both Jill and Jack

b. Jack

Explanation:

a. Doppler effect describes how the frequency of a sound wave changes with regards to an observer that has relative motion to the sound source;

The Doppler effect is given by the following formula;

For a sound that is moving away, as observed by Jill, we have;

f' = \dfrac{(v - v_0)}{(v + v_s)} \cdot f =  \dfrac{v }{(v + v_s)} \cdot f

For approaching sound, as observed by Jack, we have;

f' = \dfrac{(v + v_0)}{(v - v_s)} \cdot f =  \dfrac{v }{(v - v_s)} \cdot f

Where;

f = The sound wave's actual frequency

f' = The frequency of the moving sound to the observer

v = The speed of the sound wave

v₀ = The observer's velocity = 0

v_s = The velocity of the source (the automobile honking) of the sound wave

From the above equation, we have that the speed of sound, 'v', is the same to both the source, and the observer although the frequency, and therefore, the wavelength of the sound alternatively increases or decreases

b. From the Doppler effect equation, the person who will hear the highest frequency is given by the formula for the frequency when the sound is approaching the observer, which has the lower denominator

Therefore, given that the automobile is travelling towards Jack, jack will hear the higher frequency

5 0
3 years ago
What are the two distinct ways in which energy moves outward from the solar core to photosphere?
butalik [34]

Answer:

The energy may be carried in the form of (1) radiation, where energy travels in the form of light, and (2) convection, where energy is carried by physical motion of upwelling solar gas.

Explanation:

6 0
3 years ago
Cindy runs 500 meters every morning. It takes her 2 hours to complet
marta [7]

Answer:

250 / 2.5*10^2

Explanation:

7 0
2 years ago
A car is travelling at a constant speed of 26.5 m/s. Its tires have a radius of 72 cm. If the car slows down at a constant rate
maksim [4K]

Answer:

Magnitude of angular acceleration = -3.95 rad/s²

Explanation:

Angular acceleration is the ratio of linear acceleration and radius.

That is

        \texttt{Angular acceleration}=\frac{\texttt{Linear acceleration}}{\texttt{Radius}}\\\\\alpha =\frac{a}{r}

Radius = 72 cm = 0.72 m

Linear acceleration is rate of change of velocity.

a=\frac{11.7-26.5}{5.2}=-2.85m/s^2

Angular acceleration

        \alpha =\frac{a}{r}=\frac{-2.85}{0.72}=-3.95rad/s^2

Angular acceleration = -3.95 rad/s²  

Magnitude =  3.95 rad/s²     

4 0
3 years ago
if a ball on a string swung in a circles and string suddenly breaks.the ball will move into what direction?
Akimi4 [234]

Answer: b

Explanation: did the quiz got it right

3 0
3 years ago
Other questions:
  • If two protons and two neutrons are added to the nucleus of a carbon atom, what nucleus does it become?
    7·2 answers
  • A boy pushes a cart with a constant velocity of 0.5m/s by applying a force of 60 N. What is the total frictional force acting on
    9·1 answer
  • When a ball is thrown straight up with no air Resistance, the acceleration is in what direction ?
    9·1 answer
  • 1. How much heat energy is required to raise the temperature of a 5 kg aluminium bar
    14·1 answer
  • A photon is absorbed by an electron that is in the n = 3 state of a hydrogen atom, causing the hydrogen atom to become ionized.
    5·1 answer
  • 7. A student walks 3 blocks east, 4 blocks north, and 3 blocks west. What is the displacement of the student? (5 points)
    10·2 answers
  • Question 8 of 25
    7·1 answer
  • A 2.0-kg cart is rolling along a frictionless, horizontal track towards a 1.8-kg cart that is held initially at rest. The carts
    9·1 answer
  • Pls help me pls<br>pls use the points as my thank you ​
    7·2 answers
  • A pendulum has a mass of 3 kg and is lifted to a height of 0.3 m. What is the maximum speed of the pendulum
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!