A) \[10\,\Omega \] and \[{{\tan }^{-1}}\,\left( \frac{5}{3} \right)\]
B) \[7\,\Omega \] and \[{{45}^{\text{o}}}\]
C) \[7\,\Omega \] and \[{{\tan }^{-1}}\left( \frac{5}{3} \right)\]
D) \[10\,\Omega \,\] and \[{{\tan }^{-1}}\,\left( \frac{8}{3} \right)\]
Correct Answer: B
Solution :
| [b] \[{{e}_{0}}=283\,\,volt\,\] \[\omega =320\] |
| \[{{X}_{L}}\,=320\,\times 25\,\times {{10}^{-3}}\,=8\,\Omega \] |
| \[{{X}_{C}}\,=\frac{1}{\omega C}=\,\frac{1}{320\,\times 1000\,\times {{10}^{-6}}}\] |
| \[=\frac{1000}{320}\,=3.1\,\Omega \] |
| \[R=5\,\Omega \] |
| \[Z=\sqrt{{{R}^{2}}+{{({{X}_{L}}-{{X}_{C}})}^{2}}}\,=\sqrt{50}\,=7\,\Omega \] |
| \[\tan \phi \,=\frac{{{X}_{L}}-{{X}_{C}}}{R}\] |
| \[=1\,\,\,\,\,\,\,\,\,\,\phi ={{45}^{\text{o}}}\] |
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