what is is the ratio of the distance over which the force is applied to the distance over which the load is moved

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

andre [41]

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

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

$d=0.00184\ m$

$\boxed{d=1.84\ mm}$

8 0

2 years ago

A 2.4-kg ball falling vertically hits the floor with a speed of 2.5 m/s and rebounds with a speed of 1.5 m/s. What is the magnit

gayaneshka [121]

Answer:

9.6 Ns

Explanation:

Note: From newton's second law of motion,

Impulse = change in momentum

I = m(v-u).................. Equation 1

Where I = impulse, m = mass of the ball, v = final velocity, u = initial velocity.

Given: m = 2.4 kg, v = 2.5 m/s, u = -1.5 m/s (rebounds)

Substitute into equation 1

I = 2.4[2.5-(-1.5)]

I = 2.4(2.5+1.5)

I = 2.4(4)

I = 9.6 Ns

4 0

3 years ago

What happens if you go through a black hole ?

devlian [24]

Explanation:

The intense gravity of the black hole would pull you apart, separating your bones and muscles.

7 0

2 years ago

Read 2 more answers

Which data set has the smallest standard deviation?

hjlf

Answer:

B. 22,22,23,23,22,22,23

Explanation:

The standard deviation is a measure of dispersion or variability of a data set. In order to determine the data set that has the smallest standard deviation, we shall investigate on the ranges of the data sets given. The range of a data set is simply the difference between the maximum and minimum values in a data set. A data set that has a smaller range also has a smaller standard deviation.

From the alternatives given, the data set given by alternative B has the smallest range and consequently the smallest standard deviation.

The maximum value is 23 while the minimum is 22. The range is 1.

5 0

2 years ago

(c) A moving train has a kinetic energy of 8.1 x 10(power of 6)J.

tamaranim1 [39]

the friction force provided by the brakes is 30000 N.

<h3>What is friction force?</h3>

Friction force is the force that opposes the motion between two bodies in contact.

To calculate the average friction force provided by the brakes, we apply the formula below.

Formula:

K.E = F'd............. Equation 1

Where:

K.E = Kinetic energy of the train
F' = Friction force provided by the brakes
d = distance

Make F' the subject of the equation

F' = K.E/d............ Equation 2

From the question,

Given:

K.E = 8.1×10⁶
d = 270 m

Substitute these values into equation 2

F' = (8.1 ×10⁶)/270
F' = 30000 N

Hence, the friction force provided by the brakes is 30000 N

Learn more about friction force here: brainly.com/question/13680415

8 0

2 years ago