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A toaster oven has a resistive heating element. The average rate at which it dissipates energy as thermal energy is 1.00 kW. In the United States, emf amplitude in household circuits is Emax = 170 V and the AC oscillation rate is 60 Hz.
What is the root-mean-square current through the heating element?

Respuesta :

Answer:

I = 8.31 A

Explanation:

given,

Thermal Energy = 1 kW

Emf amplitude = 170 V

AC oscillation = 60 Hz

[tex]E_{rms} = \dfrac{E_{max}}{\sqrt{2}}[/tex]

[tex]E_{rms} = \dfrac{170}{\sqrt{2}}[/tex]

[tex]E_{rms} =120.21\ V[/tex]

Rms current is calculated as

P = VI

[tex]I =\dfrac{P}{V}[/tex]

[tex]I =\dfrac{1000}{120.21}[/tex]  

I = 8.31 A

the root-mean-square current through the heating element is equal to I = 8.31 A

shubhamchouhanvrVT

The root-mean-square current through the heating element will be

I = 8.31 A

What is root-mean-square current?

It is given that,

Thermal Energy =E= 1 kW

Emf amplitude=[tex]E_{max}[/tex]= 170 V

AC oscillation=f= 60 Hz

[tex]E_{rms} = \dfrac{E_{max} }{\sqrt{2} }[/tex]

[tex]E_{rms} =\dfrac{170}{\sqrt{2} }[/tex]

[tex]E_{rms} = 120.21V[/tex]

So the RMS current will be calculated by

[tex]P=VI[/tex]

[tex]I=\dfrac{P}{E_{rms} }[/tex]

[tex]I=\dfrac{1000}{120.21}=8.31A[/tex]

[tex]I=8.31A[/tex]

Thus the root-mean-square current through the heating element will be

I = 8.31 A

To know more about root-mean-square current follow

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