A) circuit will be capacitive if \[\omega >\frac{1}{\sqrt{L\,C}}\]
B) circuit will be inductive if \[\omega =\frac{1}{\sqrt{L\,C}}\]
C) power factor of circuit will by unity if capacitive reactance equals inductive reactance
D) current will be leading voltage if \[\omega >\frac{1}{\sqrt{L\,C}}\]
Correct Answer: C
Solution :
| The circuit will have inductive nature if \[\omega >\frac{1}{\sqrt{LC}}\,\,\left( \omega \,L>\frac{1}{\sqrt{LC}} \right).\] Hence A is false. Also if circuit has inductive nature the current will log behind voltage. Hence D is also false. If \[\omega >\frac{1}{\sqrt{LC}}\,\,\left( \omega \,L>\frac{1}{\sqrt{LC}} \right)\] the circuit will have resistance nature. Hence B is false Power factor \[\cos \phi =\frac{R}{\sqrt{{{R}^{2}}+{{\left( \omega \,L+\frac{1}{\sqrt{LC}} \right)}^{2}}}}=1\] It \[\omega \,L=\frac{1}{\omega \,C}.\] Hence C is true. |
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