Lösning 4.4:10

FörberedandeFysik

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Nuvarande version (22 mars 2018 kl. 12.58) (redigera) (ogör)
 
Rad 1: Rad 1:
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<math>U = 230 V</math> <math>P = 500 W</math> <math>R = 17,1 \Omega</math><br\>
+
<math>U = 230 \,\mathrm{V}</math>, <math>P = 500 \,\mathrm{W}</math>, <math>R = 17,1 \,\Omega</math><br\>
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<math>P = UI\cdot \cos\phi</math> <math>\cos\phi = U_R/U_Z = RI /ZI = R/Z </math><br\>
+
<math>P = UI\cdot \cos\phi</math>, <math>\cos\phi = U_R/U_Z = RI /ZI = R/Z </math><br\>
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<math>\omega = 314 rad/s</math><br\>
+
<math>\omega = 314 \,\mathrm{rad/s}</math><br\>
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<math>U = I\cdot Z</math> <math>P=UI\cdot R/Z = U^2R/Z^2</math><br\>
+
<math>U = I\cdot Z</math>, <math>P=UI\cdot R/Z = U^2R/Z^2</math><br\>
<math>500 = 230^2 \cdot 17,1/Z^2</math><br\>
<math>500 = 230^2 \cdot 17,1/Z^2</math><br\>
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<math>Z = 42,5 \Omega</math> <math>\cos\phi = 17,1/42,5 = 0,40</math><br\>
+
<math>Z = 42,5 \,\Omega</math>, <math>\cos\phi = 17,1/42,5 = 0,40</math><br\>
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<math>Z = \sqrt{R^2 + \omega ^2 L^2}</math> <math>42,5 = \sqrt{17,1^2 + 314^2L^2}</math><br\>
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<math>Z = \sqrt{R^2 + \omega ^2 L^2}</math>
 +
 
 +
<math>42,5 = \sqrt{17,1^2 + 314^2L^2}</math><br\>
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<math>L = 0,123 H</math>
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<math>L = 0,123 \,\mathrm{H}</math>

Nuvarande version

\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}

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