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\displaystyle U = 230 \,\mathrm{V}, \displaystyle P = 500 \,\mathrm{W}, \displaystyle R = 17,1 \,\Omega

\displaystyle P = UI\cdot \cos\phi, \displaystyle \cos\phi = U_R/U_Z = RI /ZI = R/Z

\displaystyle \omega = 314 \,\mathrm{rad/s}

\displaystyle U = I\cdot Z, \displaystyle P=UI\cdot R/Z = U^2R/Z^2

\displaystyle 500 = 230^2 \cdot 17,1/Z^2

\displaystyle Z = 42,5 \,\Omega, \displaystyle \cos\phi = 17,1/42,5 = 0,40

\displaystyle Z = \sqrt{R^2 + \omega ^2 L^2}

\displaystyle 42,5 = \sqrt{17,1^2 + 314^2L^2}

\displaystyle L = 0,123 \,\mathrm{H}