Total Energy Stored in Resonator Calculator

✖Permittivity of Medium is a physical quantity that describes how much electric field is allowed to pass through the medium.ⓘ Permittivity of Medium [ε_m]			+10% -10%
✖Electric Field Intensity is defined as the force experienced by a unit positive test charge placed at that point.ⓘ Electric Field Intensity [E]			+10% -10%
✖Resonator Volume refers to the physical space inside the resonating chamber. This chamber is designed to amplify and resonate sound waves, producing a specific tone or frequency.ⓘ Resonator Volume [V_r]			+10% -10%

✖Total Energy Stored in Resonator refers to the sum of all forms of energy contained within the resonant system.It is any physical or mathematical system that exhibits resonance.ⓘ Total Energy Stored in Resonator [W_e]

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Formula

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Total Energy Stored in Resonator

Formula

`"W"_{"e"} = int(("ε"_{"m"}/2*"E"^2)*x,x,0,"V"_{"r"})`

Example

`"0.000537J"=int(("0.0532μF/m"/2*("8.97V/m")^2)*x,x,0,"22.4m³")`

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Total Energy Stored in Resonator Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Energy Stored in Resonator = int((Permittivity of Medium/2*Electric Field Intensity^2)*x,x,0,Resonator Volume)
W_e = int((ε_m/2*E^2)*x,x,0,V_r)
This formula uses 1 Functions, 4 Variables

Functions Used

int - The definite integral can be used to calculate net signed area, which is the area above the x -axis minus the area below the x -axis., int(expr, arg, from, to)

Variables Used

Total Energy Stored in Resonator - (Measured in Joule) - Total Energy Stored in Resonator refers to the sum of all forms of energy contained within the resonant system.It is any physical or mathematical system that exhibits resonance.
Permittivity of Medium - (Measured in Farad per Meter) - Permittivity of Medium is a physical quantity that describes how much electric field is allowed to pass through the medium.
Electric Field Intensity - (Measured in Volt per Meter) - Electric Field Intensity is defined as the force experienced by a unit positive test charge placed at that point.
Resonator Volume - (Measured in Cubic Meter) - Resonator Volume refers to the physical space inside the resonating chamber. This chamber is designed to amplify and resonate sound waves, producing a specific tone or frequency.

STEP 1: Convert Input(s) to Base Unit

Permittivity of Medium: 0.0532 Microfarad per Meter --> 5.32E-08 Farad per Meter (Check conversion here)
Electric Field Intensity: 8.97 Volt per Meter --> 8.97 Volt per Meter No Conversion Required
Resonator Volume: 22.4 Cubic Meter --> 22.4 Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

W_e = int((ε_m/2*E^2)*x,x,0,V_r) --> int((5.32E-08/2*8.97^2)*x,x,0,22.4)

Evaluating ... ...

W_e = 0.0005369484137472

STEP 3: Convert Result to Output's Unit

0.0005369484137472 Joule --> No Conversion Required

FINAL ANSWER

0.0005369484137472 ≈ 0.000537 Joule <-- Total Energy Stored in Resonator

(Calculation completed in 00.004 seconds)

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Created by banuprakash

Dayananda Sagar College of Engineering (DSCE), Bangalore

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Heritage Insitute of technology (HITK), Kolkata

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Total Energy Stored in Resonator Formula

Total Energy Stored in Resonator = int((Permittivity of Medium/2*Electric Field Intensity^2)*x,x,0,Resonator Volume)
W_e = int((ε_m/2*E^2)*x,x,0,V_r)

What happens to the energy stored in a resonator at resonance?

At resonance, the energy stored in the resonator oscillates back and forth between the inductive and capacitive elements. In an ideal resonant circuit, the energy losses are minimized, resulting in sustained oscillations.

How to Calculate Total Energy Stored in Resonator?

Total Energy Stored in Resonator calculator uses Total Energy Stored in Resonator = int((Permittivity of Medium/2*Electric Field Intensity^2)*x,x,0,Resonator Volume) to calculate the Total Energy Stored in Resonator, The Total Energy Stored in Resonator formula is defined as sum of all forms of energy contained within the resonant system. A resonator is any physical or mathematical system that exhibits resonance, meaning it can store energy at particular frequencies or wavelengths. Total Energy Stored in Resonator is denoted by W_e symbol.

How to calculate Total Energy Stored in Resonator using this online calculator? To use this online calculator for Total Energy Stored in Resonator, enter Permittivity of Medium (ε_m), Electric Field Intensity (E) & Resonator Volume (V_r) and hit the calculate button. Here is how the Total Energy Stored in Resonator calculation can be explained with given input values -> 0.000537 = int((5.32E-08/2*8.97^2)*x,x,0,22.4).

FAQ

What is Total Energy Stored in Resonator?

The Total Energy Stored in Resonator formula is defined as sum of all forms of energy contained within the resonant system. A resonator is any physical or mathematical system that exhibits resonance, meaning it can store energy at particular frequencies or wavelengths and is represented as W_e = int((ε_m/2*E^2)*x,x,0,V_r) or Total Energy Stored in Resonator = int((Permittivity of Medium/2*Electric Field Intensity^2)*x,x,0,Resonator Volume). Permittivity of Medium is a physical quantity that describes how much electric field is allowed to pass through the medium, Electric Field Intensity is defined as the force experienced by a unit positive test charge placed at that point & Resonator Volume refers to the physical space inside the resonating chamber. This chamber is designed to amplify and resonate sound waves, producing a specific tone or frequency.

How to calculate Total Energy Stored in Resonator?

The Total Energy Stored in Resonator formula is defined as sum of all forms of energy contained within the resonant system. A resonator is any physical or mathematical system that exhibits resonance, meaning it can store energy at particular frequencies or wavelengths is calculated using Total Energy Stored in Resonator = int((Permittivity of Medium/2*Electric Field Intensity^2)*x,x,0,Resonator Volume). To calculate Total Energy Stored in Resonator, you need Permittivity of Medium (ε_m), Electric Field Intensity (E) & Resonator Volume (V_r). With our tool, you need to enter the respective value for Permittivity of Medium, Electric Field Intensity & Resonator Volume and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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