Average Power Calculator

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✖Sinusoidal Current represents the current of amplitude Io in absence of any radiation.ⓘ Sinusoidal Current [i_o]			+10% -10%
✖Radiation Resistance is the effective resistance of antenna.ⓘ Radiation Resistance [R_rad]			+10% -10%

✖Average Power is defined as the power that crosses the surface of a sphere of radius r.ⓘ Average Power [P_r]

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Formula

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Average Power

Formula

`"P"_{"r"} = 1/2*"i"_{"o"}^2*"R"_{"rad"}`

Example

`"67.8375W"=1/2*("4.5A")^2*"6.7Ω"`

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Average Power Solution

STEP 0: Pre-Calculation Summary

Formula Used

Average Power = 1/2*Sinusoidal Current^2*Radiation Resistance
P_r = 1/2*i_o^2*R_rad
This formula uses 3 Variables

Variables Used

Average Power - (Measured in Watt) - Average Power is defined as the power that crosses the surface of a sphere of radius r.
Sinusoidal Current - (Measured in Ampere) - Sinusoidal Current represents the current of amplitude Io in absence of any radiation.
Radiation Resistance - (Measured in Ohm) - Radiation Resistance is the effective resistance of antenna.

STEP 1: Convert Input(s) to Base Unit

Sinusoidal Current: 4.5 Ampere --> 4.5 Ampere No Conversion Required
Radiation Resistance: 6.7 Ohm --> 6.7 Ohm No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P_r = 1/2*i_o^2*R_rad --> 1/2*4.5^2*6.7

Evaluating ... ...

P_r = 67.8375

STEP 3: Convert Result to Output's Unit

67.8375 Watt --> No Conversion Required

FINAL ANSWER

67.8375 Watt <-- Average Power

(Calculation completed in 00.004 seconds)

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Credits

Created by Gowthaman N

Vellore Institute of Technology (VIT University), Chennai

Gowthaman N has created this Calculator and 25+ more calculators!

Verified by Ritwik Tripathi

Vellore Institute of Technology (VIT Vellore), Vellore

Ritwik Tripathi has verified this Calculator and 100+ more calculators!

< 17 Electromagnetic Radiation and Antennas Calculators

Average Power Density of Half-Wave Dipole

Go Average Power Density = (0.609*Intrinsic Impedance of Medium*Amplitude of Oscillating Current^2)/(4*pi^2*Radial Distance From Antenna^2)*sin((((Angular Frequency of Half Wave Dipole*Time)-(pi/Length of Antenna)*Radial Distance From Antenna))*pi/180)^2

Magnetic Field for Hertzian Dipole

Go Magnetic Field Component = (1/Dipole Distance)^2*(cos(2*pi*Dipole Distance/Wavelength of Dipole)+2*pi*Dipole Distance/Wavelength of Dipole*sin(2*pi*Dipole Distance/Wavelength of Dipole))

Maximum Power Density of Half-Wave Dipole

Go Maximum Power Density = (Intrinsic Impedance of Medium*Amplitude of Oscillating Current^2)/(4*pi^2*Radial Distance From Antenna^2)*sin((((Angular Frequency of Half Wave Dipole*Time)-(pi/Length of Antenna)*Radial Distance From Antenna))*pi/180)^2

Power Radiated by Half-Wave Dipole

Go Power Radiated by Half-wave Dipole = ((0.609*Intrinsic Impedance of Medium*(Amplitude of Oscillating Current)^2)/pi)*sin(((Angular Frequency of Half Wave Dipole*Time)-((pi/Length of Antenna)*Radial Distance From Antenna))*pi/180)^2

Power that Crosses Surface of Sphere

Go Power Crossed at Sphere Surface = pi*((Amplitude of Oscillating Current*Wavenumber*Short Antenna Length)/(4*pi))^2*Intrinsic Impedance of Medium*(int(sin(Theta)^3*x,x,0,pi))

Electric Field due to N Point Charges

Go Electric Field due to N Point Charges = sum(x,1,Number of Point Charges,(Charge)/(4*pi*[Permitivity-vacuum]*(Distance from Electric Field-Charge Distance)^2))

Poynting Vector Magnitude

Go Poynting Vector = 1/2*((Dipole Current*Wavenumber*Source Distance)/(4*pi))^2*Intrinsic Impedance*(sin(Polar Angle))^2

Total Radiated Power in Free Space

Go Total Radiated Power in Free Space = 30*Amplitude of Oscillating Current^2*int((Dipole Antenna Pattern Function)^2*sin(Theta)*x,x,0,pi)

Radiated Resistance

Go Radiation Resistance = 60*(int((Dipole Antenna Pattern Function)^2*sin(Theta)*x,x,0,pi))

Time Average Radiated Power of Half-Wave Dipole

Go Time Average Radiated Power = (((Amplitude of Oscillating Current)^2)/2)*((0.609*Intrinsic Impedance of Medium)/pi)

Polarization

Go Polarization = Electric Susceptibility*[Permitivity-vacuum]*Electric Field Strength

Radiation Resistance of Half-Wave Dipole

Go Radiation Resistance of Half-wave Dipole = (0.609*Intrinsic Impedance of Medium)/pi

Directivity of Half-Wave Dipole

Go Directivity of Half Wave Dipole = Maximum Power Density/Average Power Density

Electric Field for Hertzian Dipole

Go Electric Field Component = Intrinsic Impedance*Magnetic Field Component

Radiation Efficiency of Antenna

Go Radiation Efficiency of Antenna = Maximum Gain/Maximum Directivity

Average Power

Go Average Power = 1/2*Sinusoidal Current^2*Radiation Resistance

Radiation Resistance of Antenna

Go Radiation Resistance = 2*Average Power/Sinusoidal Current^2

Average Power Formula

Average Power = 1/2*Sinusoidal Current^2*Radiation Resistance
P_r = 1/2*i_o^2*R_rad

How does the Average power of a spherical electromagnetic wave change with distance from the source?

The Avergae power of a spherical electromagnetic wave is inversely proportional to the square of the distance from the source. This means that as the distance from the source increases, the power density decreases.

How to Calculate Average Power?

Average Power calculator uses Average Power = 1/2*Sinusoidal Current^2*Radiation Resistance to calculate the Average Power, The Average Power formula states that the average power of a spherical electromagnetic wave is proportional to the square of the product of the Current of the wave and Radiation Resistance. Average Power is denoted by P_r symbol.

How to calculate Average Power using this online calculator? To use this online calculator for Average Power, enter Sinusoidal Current (i_o) & Radiation Resistance (R_rad) and hit the calculate button. Here is how the Average Power calculation can be explained with given input values -> 67.8375 = 1/2*4.5^2*6.7.

FAQ

What is Average Power?

The Average Power formula states that the average power of a spherical electromagnetic wave is proportional to the square of the product of the Current of the wave and Radiation Resistance and is represented as P_r = 1/2*i_o^2*R_rad or Average Power = 1/2*Sinusoidal Current^2*Radiation Resistance. Sinusoidal Current represents the current of amplitude Io in absence of any radiation & Radiation Resistance is the effective resistance of antenna.

How to calculate Average Power?

The Average Power formula states that the average power of a spherical electromagnetic wave is proportional to the square of the product of the Current of the wave and Radiation Resistance is calculated using Average Power = 1/2*Sinusoidal Current^2*Radiation Resistance. To calculate Average Power, you need Sinusoidal Current (i_o) & Radiation Resistance (R_rad). With our tool, you need to enter the respective value for Sinusoidal Current & Radiation Resistance 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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