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An electric dryer with an equivalent series resistance and inductance of values 13 ΩΩ and 46 mHmH is plugged into a standard 240V(RMS) 60Hz wall socket. You may assume the phase of the source voltage is zero. a) Calculate the load current.

Respuesta :

Given:

R = 13 Ω

L = 46 mH

V = 240 V(rms)

f = 60 Hz

Formula used:

[tex]I_{L} = \frac{V}{R + jX_{L} }[/tex]

[tex]X_{L} = 2\pi fL[/tex]

Solution:

Now, using the above formula for [tex]X_{L}[/tex]:

[tex]X_{L} = 2\pi\times 60\times 46\times 10^{-3} [/tex] = 17.34 Ω

From the above formula for  [tex]I_{L}[/tex]:

[tex]I_{L} = \frac{240\angle0}{13 + j17.34 }[/tex]

[tex]I_{L}[/tex] = (6.64 - j8.86) A = [tex]11.07\angle-53.14^{\circ}[/tex] A

[tex]i_{L}(t)[/tex] = [tex]\sqrt{2}\times 11.07cos(2\pi \times 60t - 53.14)[/tex] A

[tex]i_{L}(t)[/tex] = 15.65cos(376.99t - 53.14)A

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