A) \[0.08\text{ }H\]
B) \[0.04\text{ }H\]
C) \[0.02\text{ }H\]
D) \[1H\]
Correct Answer: A
Solution :
| A coil consists of an inductance (L) and a resistance (R). |
| In dc only resistance is effective. Hence, \[R=\frac{V}{i}=\frac{12}{4}=3\Omega \] |
| In ac, \[{{i}_{rms}}=\frac{{{V}_{rms}}}{Z}=\frac{{{V}_{rms}}}{\sqrt{{{R}^{2}}+{{\omega }^{2}}{{L}^{2}}}}\] |
| \[\therefore \,\,{{L}^{2}}=\frac{1}{{{\omega }^{2}}}\left[ {{\left( \frac{{{V}_{rms}}}{{{i}_{rms}}} \right)}^{2}}-{{R}^{2}} \right]\] |
| \[\Rightarrow \,\,\,\,L=\frac{1}{\omega }\,\sqrt{{{\left( \frac{{{V}_{rms}}}{{{i}_{rms}}} \right)}^{2}}-{{R}^{2}}}=\frac{1}{50}\sqrt{{{\left( \frac{12}{2.4} \right)}^{2}}-{{(3)}^{2}}}\] |
| \[=0.08\] henry |
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