Question

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Q.6. The resonant frequency of a series LCR with resistor of resistance R, inductor of inductance L and capacitor of capacitance C is $\nu$. What is its resonant frequency when inductance and capacitance both doubled?

Answer 1

Dear Student,


$$\begin{gathered} resonantfrequency\nu =\frac{1}{2\mathrm{\pi }\sqrt{\mathrm{LC}}} \\ resonantfrequencyforinduc\tan ceandcapaci\tan ceisdouble \\ \nu \text{'}=\frac{1}{2\mathrm{\pi }\sqrt{\left(2L\right)\left(2C\right)}}=\frac{1}{4\mathrm{\pi }\sqrt{\mathrm{LC}}}=\frac{\nu }{2} \\ sotheresosnantfrequencybecomeshalf. \\ Regards \end{gathered}$$