You have a small electromagnet that consumes 260 W from a residential circuit de

Question

You have a small electromagnet that consumes 260 W from a residential circuit delivering 110 V rms at 50.0 Hz. Using your AC multimeter, you determine that the unit draws 3.97 A rms. What is the internal resistance of the electromagnet? What is the inductance of the electromagnet?

Explanation / Answer

P = I^2R 260 = (3.97)^2R ---> R = 260/((3.97)^2) = 16.497 ohms --- solution . z = v/I sqrt ( R^2 + (wL)^2) = 110/3.97 . Square both sides , and we get : R^2 + (wL)^2 = (110/3.97)^2 . Subtract R^2 from both sides : (wL)^2 = (110/3.97)^2 - R^2 . Take the square root of both sides : wL = sqrt ( (110/3.97)^2 - R^2) . We have the radian frequency is --- w =2(pi)f = 2(pi)(50) = 100pi : 2(pi)f L = sqrt ((110/3.97)^2 - R^2) . We thus divide both sides by w = 100pi : L = sqrt ( (100/3.97)^2 - R^2)/ (100pi) = .07086 henries --- solution .

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