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Page 1 Series resonance For resonance ? ? ? m I Z 0 ? ? ? ? ? ? ? 1 Z R j L c ? ? ? ? ? ? 1 1 L rad s c LC The frequency at which impedance of circuits is purely resistive is called resonant frequency. ?? 0 1 rad s LC At resonance S V I R ? ?? RS V IR V ?? ?? ?? ?? ? ? ? ? S L o o V V j LI j L R ?? ?? ?? ?? ?? ?? ?? S c 0o V jj VI c C R At ? ? ? ? 0 L C ; X X , net reactance is capacitive so circuits operates at leading pf. At ? ? ? ? 0 L C ; X X , net reactance is zero, so circuits operates at unity pf. At ? ? ? ? 0 L C ; X X , net reactance is inductive, so circuits operates at lagging pf. Bandwidth: range of frequency for which power delivered to R is half of power at resonance. R Bw L ? Quality factor ? ? ? 22 22 LC 11 I X I X Reactive power 22 Q 11 Average power I R I R 22 ? ? ? LC XX 1L Q R R R C Page 2 Series resonance For resonance ? ? ? m I Z 0 ? ? ? ? ? ? ? 1 Z R j L c ? ? ? ? ? ? 1 1 L rad s c LC The frequency at which impedance of circuits is purely resistive is called resonant frequency. ?? 0 1 rad s LC At resonance S V I R ? ?? RS V IR V ?? ?? ?? ?? ? ? ? ? S L o o V V j LI j L R ?? ?? ?? ?? ?? ?? ?? S c 0o V jj VI c C R At ? ? ? ? 0 L C ; X X , net reactance is capacitive so circuits operates at leading pf. At ? ? ? ? 0 L C ; X X , net reactance is zero, so circuits operates at unity pf. At ? ? ? ? 0 L C ; X X , net reactance is inductive, so circuits operates at lagging pf. Bandwidth: range of frequency for which power delivered to R is half of power at resonance. R Bw L ? Quality factor ? ? ? 22 22 LC 11 I X I X Reactive power 22 Q 11 Average power I R I R 22 ? ? ? LC XX 1L Q R R R C Parallel Resonance ? ? ? ? ? 1 1 Y j C R jL At resonance ? ? ? m I Y 0 ?? o 1 rad s LC ? S At resona e V c I n R ? RS II ?? ?? S L 00 IR V I j L j L ? ? ? ? ? ? ? ? C 0 S 0 I V j C I R j C ? Bandwidth 1 RC ? Reactive P Quality fa ower Q Average ctor, Power 2 2 C L 22 LC V V 2X 2X R R C QR X X L VV 2R 2R ? ? ? ? ?Read More
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