The current at resonance in a series L-C-R circuit is 0.2mA. If the applied voltage is 250mV at a frequency of 100 kHz and the circuit capacitance is 0.04 microfrad . Find the circuit resistance and inductance

Answers

Answer 1

Answer:

The resistance of the circuit is 1250 ohmsThe inductance of the circuit is 0.063 mH.

Explanation:

Given;

current at resonance, I = 0.2 mA

applied voltage, V = 250 mV

resonance frequency, f₀ = 100 kHz

capacitance of the circuit, C = 0.04 μF

At resonance, capacitive reactance ([tex]X_c[/tex]) is equal to inductive reactance ([tex]X_l[/tex]),

[tex]Z = \sqrt{R^2 + (X_ l - X_c)^2} \\\\But \ X_l= X_c\\\\Z = R[/tex]

Where;

R is the resistance of the circuit, calculated as;

[tex]R = \frac{V}{I} \\\\R = \frac{250 \ \times \ 10^{-3}}{0.2 \ \times \ 10^{-3}} \\\\R = 1250 \ ohms[/tex]

The inductive reactance is calculated as;

[tex]X_l = X_c = \frac{1}{\omega C} = \frac{1}{2\pi f_o C} = \frac{1}{2\pi (100\times 10^3)(0.04\times 10^{-6} ) } = 39.789 \ ohms\\[/tex]

The inductance is calculated as;

[tex]X_l = \omega L = 2\pi f_o L\\\\L = \frac{X_l}{2\pi f_o}\\\\L = \frac{39.789}{2\pi (100 \times 10^3)} \\\\L= 6.3 \ \times \ 10^{-5} \ H\\\\L = 0.063 \times \ 10^{-3} \ H\\\\L = 0.063 \ mH[/tex]


Related Questions

What should Kimi have done to ensure that she was acting legally and ethically?

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Answer:

Kimi have done to ensure that she was acting legally and ethically by following the measure that are discussed below in detail.

Explanation:

Legal measures are those measures that are outlined in regulatory laws. Ethical measures are based on the human postulates of morality and wrongdoing. The distinctions between them are these: Legal measures are based on transcribed law, while ethical measures are based on human rights and violations.

It is preferable not to drive a vehicle in reverse if you have an obstructed view, but if you do, make sure:

Answers

Answer:

While driving in reverse gear it necessary to have reverse audible alarm , a spotter and a rear view mirror.

Explanation:

It is prefer that to not drive a vehicle in reverse. But if we are driving in reverse gear it is necessary to have a reverse audible alarm , a spotter and a rear view mirror.

A small probe P is gently forced against the circular surface with a vertical force F as shown . Determine the n- and t-components of this force as functions of the horizontal positions.

Answers

This question is incomplete, its missing an image which will be uploaded along this Answer.

Answer:

the normal component of force F_n is F((√(r²-s²)) / r)

the tangential component of force F_t is F(s/r)

Explanation:

Given the data in the image;

from the free body diagram, we write the expression for ∅

sin∅ = s/r

cos∅ = (√(r²-s²)) / r

now expression for normal component of force is;

F_n = Fcos∅

we substitute

F_n = F((√(r²-s²)) / r)

Therefore, the normal component of force F_n is F((√(r²-s²)) / r)

Also for force F_t

F_t = Fsin∅

we substitute

F_t = F(s/r)

Therefore, the tangential component of force F_t is F(s/r)

Two technicians are discussing hd-obd for trucks technician a says that the simplest most familiar definition is the diagnostic function of electronic control system to identify or self-diagnose system fault and report fault codes technician b says automotive and light duty truck versions of OBD is called OBD2 who is correct

Answers

Answer:

Two technicians are discussing HD-OBD for trucks

Technician a says that the simplest most familiar definition is the diagnostic function of electronic control system to identify or self-diagnose system fault and report fault codes.

Technician A is correct.

Explanation:

Onboard Diagnostics (OBD) is a vehicle's self-diagnostic tool which enables technicians to access the diagnostic information for the purpose of performance monitoring and analyzing repair needs of vehicles.  OBD2 is the diagnostic system that is included in every vehicle made after 1996.  The diagnostics can check the engine and other vehicle systems and also communicate possible vehicular glitches that happen.

Find the derivative of y = sin(ln(5x2 − 2x))

Answers

Answer:

[tex]y = \cos[\ln x + \ln (5\cdot x - 2)]\cdot \left(\frac{1}{x} + \frac{5}{5\cdot x-2} \right)[/tex]

Explanation:

Let [tex]y = \sin[\ln(5\cdot x^{2}-2\cdot x)][/tex] and we proceed to find the derivative by the following steps:

1) [tex]y = \sin[\ln(5\cdot x^{2}-2\cdot x)][/tex] Given

2) [tex]y = \sin [\ln[x\cdot (5\cdot x - 2)]][/tex] Distributive property

3) [tex]y = \sin[\ln x + \ln (5\cdot x - 2 )][/tex] [tex]\ln (a\cdot b) = \ln a + \ln b[/tex]

4) [tex]y = \cos[\ln x + \ln (5\cdot x - 2)]\cdot \left(\frac{1}{x} + \frac{5}{5\cdot x-2} \right)[/tex]  [tex]\frac{d}{dx} (\sin x) = \cos x[/tex]/[tex]\frac{d}{dx}(\ln x) = \frac{1}{x}[/tex]/[tex]\frac{d}{dx}(c\cdot x^{n}) = n\cdot c\cdot x^{n-1}[/tex]/Rule of chain/Result

please help me solve this​

Answers

Answer:

Following are the solution to this question:

Explanation:

[tex]\to \Sigma F_x = ma_x \\\\\to 3200 t^2 -440 (9.81) (\frac{8}{17}) = 440 (a) \\\\\to 3200 t^2 -2031.24 = 440 (a)\\\\\to a= 7.27t^2 -4.616\\\\\to dv=a.dt \\\\\to \int^{v}_{2} dv = \int^{2}_{0} (7.27t^2 -4.616) dt\\\\\to v-2 = 7.27 \frac{t^3}{3} - 4.616 t^{2}_{0}\\\\\to v-2 = 7.27 \frac{2^3}{3} - 4.616 {2} \\\\\to v-2 = 10.154\\\\\to v= 12.154 \ \frac{m}{s}\\[/tex]

one number is 11 more than another number. find the two number if three times the larger number exceeds four times the smaller number by 4​

Answers

Answer:

a = 40

b = 29

Explanation:

Give a place holder for the numbers that we don't know.

Lets call the two numbers a and b.

From the given info, we can write an expression and solve it:

"one number is 11 more than another number"

a = 11 + b

from this, we know that a > b.

''three times the larger number exceeds four times the smaller number by 4"

3a = 4b + 4

Now we have 2 equations, we can use them to solve using whatever method you want.

a = 11 + b

3a = 4b + 4

I will be using matrices RREF to solve for this.

a - b = 11

3a - 4b = 4

[tex]\begin{bmatrix}1 & -1 & 11\\3 & -4 & 4 \end{bmatrix}[/tex]

[tex]\begin{bmatrix}1 & 0 & 40\\0 & 1 & 29 \end{bmatrix}[/tex]

a = 40

b = 29

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Answers

The one that has Ben cited the most and which most directly relates to the topic it is pertaining to.

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a:4.546
b:3.785
c.5.456
d.7.385​

Answers

Answer:

c

Explanation:

I live in britian

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Answer:

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Explanation:

Answer: That happens to me too sometimes. I hate when people give the wrong answers...like if u don't know the answer, then don't respond

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Can u answer myn and if u do I’ll do urs
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