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Derive an expression for resonant frequency of series circuit containing inductor, capacitor and resistor. |
Answer» SOLUTION : Series LCR circuit is said to be in resonance when CURRENT through the circuit is maximum. In a series LCR circuit current amplitude is given by `i_(m)=(V_(m))/(Z)` `i_(m)=(V_(m))/(sqrt(R^(2)+(X_( C )-X_(L))^(2)))` where `X_( C )=(1)/(omegaC)` and `X_(L)=omega_(L)` If FREQUENCY is varied, at particular angular frequency `omega_(0)` the condition `X_( C )=X_(L)` is achieved, this condition is called resonance, `(1)/(omega_(o)C)=omega_(0)L` `:." "omega_(0)=(1)/(sqrt(LC))` `2pi v_(o)=(1)/(sqrt(LC))""(because omega_(0)=2pi v_(0))` `v_(0)=(1)/(2pi sqrt(LC))` is called resonant frequency |
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