A) Circuit will be capacitive if \[\omega >\frac{1}{\sqrt{LC}}\]
B) Circuit will be inductive if \[\omega =\frac{1}{\sqrt{LC}}\]
C) Power factor of circuit will be unity if capacitive reactance equals inductive reactance
D) Current will be leading voltage if \[\omega >\frac{1}{\sqrt{LC}}\]
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 lag behind voltage. Hence D also false |
| If \[\omega >\frac{1}{\sqrt{LC}}\left( \omega L=\frac{1}{\omega C} \right)\] the circuit will have resistance nature. Hence B is false |
| Power factor \[\cos \phi =\frac{R}{\sqrt{{{R}^{2}}+{{\left( \omega L-\frac{1}{\omega C} \right)}^{2}}}}=1\] |
| If \[\omega L=\frac{1}{\omega C}.\] |
| Hence C is true |
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