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A series LCR circuit with L = 0.12 H, C = 480 pF, R = 23 Omega is connected to a 230 V variable frequency supply. For which frequencies of the source is the power transferred to the circuit half power at resonant frequency ? What is the current amplitude at these frequencies ? |
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Answer» Solution :Inductance `L = 0.12 H`, Capacitance `C = 480 NF = 480xx10^(-9)F` Resistance `R = 23 Omega` The rms value of voltage VRMS = 230 V Power transferred to the circuit is half the power at RESONANT frequency. `Delta omega=(R )/(2L)=(23)/(2xx0.12)=95.83` rad/s `Delta V=(Delta W)/(2pi)=15.2Hz` The FREQUENCIES at which power transferred is half `V=V_(0)pm Delta V=663.48 pm 15.26` So, frequencies are 448.3Hz and 678.2Hz, the maximum current `I=(I_(0))/(sqrt(2))=(14.14)/(sqrt(2))=10A` |
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