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
Vesnalui [34]
3 years ago
11

A resistor R, inductor L, and capacitor C are connected in series to an AC source of rms voltage ΔV and variable frequency. If t

he operating frequency is twice the resonance frequency, find the energy delivered to the circuit during one period. (Use the following as necessary: the rms voltage ΔV, R, L, and C.)
Physics
1 answer:
Alexandra [31]3 years ago
3 0

Answer:E=\frac{\pi R\left ( \Delta V\right )^2\sqrt{LC}}{\left ( R^2+\frac{9}{4}\left (\frac{L}{C} \right )\right )}

Explanation:

We know resonant frequency is given by

\omega_0=\frac{1}{\sqrt{LC}}

and the operating frequency is given by

\omega =2\omega_0=\frac{2}{\sqrt{LC}}

The capacitance reactance is given by

X_c=\frac{1}{\omega C}=\frac{\sqrt{LC}}{2C}=\frac{1}{2}\sqrt{\frac{L}{C}}

inductive reactance is given by

X_L=\omega L=\left ( \frac{2}{\sqrt{LC}}\right )L=2\sqrt{\frac{L}{C}}

Thus impedance is

Z=\left ( R^2+\left (X_L-X_C \right )^2 \right )^\frac{1}{2}

Z=\left ( R^2+\left (2\sqrt{\frac{L}{C}}-\frac{1}{2}\sqrt{\frac{L}{C}} \right )^2 \right )^\frac{1}{2}

Z=\left ( R^2+\frac{9}{4}\left ( \frac{L}{C} \right ) \right )^\frac{1}{2}

The average power delivered is

P_{avg.}=\frac{\Delta V^2}{Z}cos\phi =\frac{\left ( \Delta V\right )^2}{Z}\left (\frac{R}{Z} \right )

P_{avg.}=\frac{\left (\Delta V \right )^2R}{\left ( R^2+\frac{9}{4}\left (\frac{L}{C} \right )\right )}

Energy Delivered in one cycle is given by

E=P_{avg}T

E=\frac{\left (\Delta V \right )^2R}{\left ( R^2+\frac{9}{4}\left (\frac{L}{C} \right )\right )}\left ( \frac{2\pi }{\frac{2}{\sqrt{LC}}}\right )

E=\frac{\pi R\left ( \Delta V\right )^2\sqrt{LC}}{\left ( R^2+\frac{9}{4}\left (\frac{L}{C} \right )\right )}              

You might be interested in
Now assume that the boat is subject to a drag force fd due to water resistance. is the component of the total momentum of the sy
DochEvi [55]
Based on the given details with this question, I can say that the direction of motion is not conserved. This is because the boat is subjected to an external force because of water resistance. So, the answer for this question would be NO.
4 0
3 years ago
Read 2 more answers
A virtual image seems to come from
Alex_Xolod [135]

behind the mirror

Contrary to real images, virtual images cannot be illustrated on a screen. The optical image will appear at the point of divergence ( of outgoing rays from a point). It is an optical image that seems to be projected from behind the mirror.

4 0
3 years ago
Read 2 more answers
The weight y of a fiddler crab is directly proportional to the 1.25 power of the weight x of its claws. A crab with a body weigh
frez [133]

Answer:

The weight of body is 1.3040 gram.

Explanation:

Given that,

The weight y of a fiddler crab is directly proportional to the 1.25 power of the weight x of its claws.

Suppose a crab with a body weight of 1.8 gram has claws weighing 1.1 gram.

Estimate the weight of a fiddler crab with claws weighing 0.85 gram.

Determine the weight of crab body

We need to calculate the value of proportional constant

y\propto x^{1.25}

y=kx^{1.25}

k=\dfrac{y}{x^{1.25}}

Put the value into the formula

k=\dfrac{1.8}{1.1^{1.25}}

k=1.5978

We need to calculate the crab weight

y=kx^{1.25}

Here, x = 0.85 g

Put the value into the formula

y=1.5978\times(0.85)^{1.25}

y=1.3040\ gram

Hence, The weight of body is 1.3040 gram.

7 0
4 years ago
What can you assume has happened if an electron moves to a higher energy level
tresset_1 [31]

The extra energy that the electron suddenly has had to
come from somewhere, so I can assume that one of
two things happened:

either 1).  A photon passed by and the electron absorbed it.

      or 2).  Somebody hooked up a battery or a generator in
such a way that the electron was bathed in a field of electrostatic
potential, and suddenly had the get-up-and-go to jump to a higher
energy level, and possibly even to leave its atom completely and
zip over to a neighbor atom.

7 0
3 years ago
Read 2 more answers
(forces and motion) in 2-3 sentences explain why velocity (or speed) is interesting
Mariulka [41]
‘velocity’ refers to how fast an object is moving ‘in a particular direction’. speed is only how fast something is moving and velocity is how fast something is moving AND the direction. (hope this helps)
6 0
3 years ago
Other questions:
  • ? What is the magnitude of force required to accelerate a car of mass 1.7 × 103 kilograms by 4.75 meters/second2
    9·2 answers
  • based on how the book describes a heat pump in sec 16.3 how does a heat pump prove law of conservation of energy
    11·1 answer
  • Give reason the si syetem of units is better than the mks system​
    12·1 answer
  • What is the mass of a book that weighs 234 N?
    7·1 answer
  • A dolphin in an aquatic show jumps straight up out of the water at a velocity of 11.8 m/s. The magnitude of the gravitational ac
    12·1 answer
  • What are the three most important types of units in radiobiology? Explain the meaning of each.
    8·1 answer
  • The same car now travels on a straight track and goes over a hill with radius 101 m at the top. What is the maximum speed that t
    8·1 answer
  • 1. A 12kg mass is sliding down a ramp at a 30° angle from the horizontal. The coefficient of friction between the
    11·1 answer
  • Why is no energy required in passive transport?
    15·1 answer
  • Developed countries typically have _______.
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!