A 250mH inductor is connected across an ac source of delta V

A 250-mH inductor is connected across an ac source of delta V_m = 90.0 V. At what frequency will the inductive reactance equal 20.0 ohm? What is the rms value of current in the inductor at the frequency found in part (a)?

Solution

the inductive reactance is,

X_L = 2*pi*fL

Thus, the required frequency is,

f = X_L / 2*pi*L = 20 / 2*pi*250x10^-3 = 12.74 Hz

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the rms current is,

Irms = dVrms/R = dVmax/sqrt[2]*R = 90 / sqrt[2]*20 = 3.18 A