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A series resonant circuit contains L_(1),R_(1) and C_(1). The resonant frequency is f. Another series resonant circuit contains L_(2), R_(2) and C_(2). The resonant frequency is also f. If these two circuits are connected in series, calculate the resonant frequency. |
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Answer» Solution :Given that resonant FREQUENCY (f) `=(1)/(2pi SQRT(L_(1)C_(1)))=(1)/(2pi sqrt(L_(2)C_(2)))` `L_(1)C_(1)=L_(2)C_(2)` `L_(1)=(L_(2)C_(2))/(C_(1))` …..(1) When these TWO CIRCUITS are connected in series The TOTAL inductance `L = L_(1)+L_(2)` Total capacitance is given by `(1)/(C )=(1)/(C_(1))+(1)/(C_(2))` (or) `C=(C_(1)C_(2))/(C_(1)+C_(2))` The resonant frequency of combinedcircuit is given by `f' = (1)/(2pi sqrt(LC))=(1)/(2pi sqrt((L_(1)+L_(2))(C_(1)C_(2))/(C_(1)+C_(2))))` `= (1)/(2pi sqrt(((L_(2)C_(2))/(C_(1))+L_(2))(C_(1)C_(2))/(C_(1)+C_(2))))` `= (1)/(2pi sqrt(L_(2)((C_(2)+C_(1))/(C_(1)))(C_(1)C_(2))/(C_(1)+C_(2))))` `= (1)/(2pi sqrt(L_(2)C_(2)))` `f' = f` |
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