Average Power Loss in Resonator Calculator

✖Surface Resistance of resonator is the ratio of applied voltage to current flowing from two electrodes.ⓘ Surface Resistance of resonator [R_s]			+10% -10%
✖Tangential Magnetic Intensity Peak Value is the peak value of the tangential magnetic intensity which is a magnetic field strength.ⓘ Tangential Magnetic Intensity Peak Value [H_t]			+10% -10%
✖Radius of resonator is the radius which is used to calculate the average power loss in resonator.ⓘ Radius of resonator [r_r]			+10% -10%

✖Average Power Loss in Resonator can be evaluated by integrating the power density over the inner surface of the resonator.ⓘ Average Power Loss in Resonator [P]

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Formula

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Average Power Loss in Resonator

Formula

`"P" = ("R"_{"s"}/2)*(int((("H"_{"t"})^2)*x,x,0,"r"_{"r"}))`

Example

`"20.8W"=("5.2Ω"/2)*(int((("2A/m")^2)*x,x,0,"2m"))`

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Average Power Loss in Resonator Solution

STEP 0: Pre-Calculation Summary

Formula Used

Average Power Loss in Resonator = (Surface Resistance of resonator/2)*(int(((Tangential Magnetic Intensity Peak Value)^2)*x,x,0,Radius of resonator))
P = (R_s/2)*(int(((H_t)^2)*x,x,0,r_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

Average Power Loss in Resonator - (Measured in Watt) - Average Power Loss in Resonator can be evaluated by integrating the power density over the inner surface of the resonator.
Surface Resistance of resonator - (Measured in Ohm) - Surface Resistance of resonator is the ratio of applied voltage to current flowing from two electrodes.
Tangential Magnetic Intensity Peak Value - (Measured in Ampere per Meter) - Tangential Magnetic Intensity Peak Value is the peak value of the tangential magnetic intensity which is a magnetic field strength.
Radius of resonator - (Measured in Meter) - Radius of resonator is the radius which is used to calculate the average power loss in resonator.

STEP 1: Convert Input(s) to Base Unit

Surface Resistance of resonator: 5.2 Ohm --> 5.2 Ohm No Conversion Required
Tangential Magnetic Intensity Peak Value: 2 Ampere per Meter --> 2 Ampere per Meter No Conversion Required
Radius of resonator: 2 Meter --> 2 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P = (R_s/2)*(int(((H_t)^2)*x,x,0,r_r)) --> (5.2/2)*(int(((2)^2)*x,x,0,2))

Evaluating ... ...

P = 20.8

STEP 3: Convert Result to Output's Unit

20.8 Watt --> No Conversion Required

FINAL ANSWER

20.8 Watt <-- Average Power Loss in Resonator

(Calculation completed in 00.020 seconds)

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Credits

Created by Zaheer Sheik

Seshadri Rao Gudlavalleru Engineering College (SRGEC), Gudlavalleru

Zaheer Sheik has created this Calculator and 10+ more calculators!

Verified by Dipanjona Mallick

Heritage Insitute of technology (HITK), Kolkata

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Average Power Loss in Resonator Formula

Average Power Loss in Resonator = (Surface Resistance of resonator/2)*(int(((Tangential Magnetic Intensity Peak Value)^2)*x,x,0,Radius of resonator))
P = (R_s/2)*(int(((H_t)^2)*x,x,0,r_r))

What is the Power Loss in Resonator?

In an ideal resonator, all the energy that is input into the system would oscillate back and forth indefinitely without any loss. However, in practical resonators, there are various mechanisms that lead to power loss. The total power loss in a resonator is typically quantified in terms of power dissipated per unit time, often measured in watts (W). Minimizing power loss is important for maximizing the efficiency and performance of resonators in various applications. This often involves careful selection of materials, design optimization, and minimizing losses through proper impedance matching and isolation techniques.

How to Calculate Average Power Loss in Resonator?

Average Power Loss in Resonator calculator uses Average Power Loss in Resonator = (Surface Resistance of resonator/2)*(int(((Tangential Magnetic Intensity Peak Value)^2)*x,x,0,Radius of resonator)) to calculate the Average Power Loss in Resonator, The Average Power Loss in Resonator formula refers to the amount of power dissipated or lost within the resonator over a given time period. Average Power Loss in Resonator is denoted by P symbol.

How to calculate Average Power Loss in Resonator using this online calculator? To use this online calculator for Average Power Loss in Resonator, enter Surface Resistance of resonator (R_s), Tangential Magnetic Intensity Peak Value (H_t) & Radius of resonator (r_r) and hit the calculate button. Here is how the Average Power Loss in Resonator calculation can be explained with given input values -> 20.8 = (5.2/2)*(int(((2)^2)*x,x,0,2)).

FAQ

What is Average Power Loss in Resonator?

The Average Power Loss in Resonator formula refers to the amount of power dissipated or lost within the resonator over a given time period and is represented as P = (R_s/2)*(int(((H_t)^2)*x,x,0,r_r)) or Average Power Loss in Resonator = (Surface Resistance of resonator/2)*(int(((Tangential Magnetic Intensity Peak Value)^2)*x,x,0,Radius of resonator)). Surface Resistance of resonator is the ratio of applied voltage to current flowing from two electrodes, Tangential Magnetic Intensity Peak Value is the peak value of the tangential magnetic intensity which is a magnetic field strength & Radius of resonator is the radius which is used to calculate the average power loss in resonator.

How to calculate Average Power Loss in Resonator?

The Average Power Loss in Resonator formula refers to the amount of power dissipated or lost within the resonator over a given time period is calculated using Average Power Loss in Resonator = (Surface Resistance of resonator/2)*(int(((Tangential Magnetic Intensity Peak Value)^2)*x,x,0,Radius of resonator)). To calculate Average Power Loss in Resonator, you need Surface Resistance of resonator (R_s), Tangential Magnetic Intensity Peak Value (H_t) & Radius of resonator (r_r). With our tool, you need to enter the respective value for Surface Resistance of resonator, Tangential Magnetic Intensity Peak Value & Radius of resonator 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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