A) Frequency must be increased and current after the change is 10 A
B) Frequency must be decreased and current after the change is 10 A
C) Frequency must be decreased and current is same as that of initial value
D) The given information is insufficient to conclude anything
Correct Answer: A
Solution :
| Initially at resonance: \[{{X}_{L}}={{X}_{E}}\]\[\Rightarrow \]\[Z=R\] |
| \[\therefore \]\[{{i}_{0}}=\frac{{{\varepsilon }_{0}}}{R}=10\sqrt{2}\,A\] |
| After increasing frequency:\[{{X}_{L}}>{{X}_{c}}\] |
| \[\omega \,L>1/\omega \,C\] |
| \[\omega >\frac{1}{\sqrt{LC}}\]\[\Rightarrow \]\[\omega >{{\omega }_{0}}\](i.e., frequency increases) and \[i'=\frac{{{\varepsilon }_{0}}}{\sqrt{{{R}^{2}}+{{X}^{2}}}}=\frac{{{\varepsilon }_{0}}}{\sqrt{2R}}={{i}_{0}}/\sqrt{2}=10\,\,amp.\] |
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