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https://texercises.com/exercise/rlc-series-circuit-1/
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Exercise:
A RO resistor a LO inductor and a CO capacitor are connected in series to an ac voltage supply. abcliste abc Derive a formal expression for the angular frequency at which the impedance of an RLC series circuit is equal to twice the resistance: ZomegaR. abc Calculate the numerical value of the angular frequency in a. abcliste

Solution:
abcliste abc The condition can be written as Zomega sqrtR^+leftomega L-fracomega Cright^ R Longrightarrow R^+leftomega L-fracomega Cright^ R^ Longrightarrow omega L-fracomega C pm sqrt R This leads to the quadratic omega^ L mp omega sqrt R-fracC with the positive solutions omega_ fracpmsqrtR+sqrt R^+dfracLC L abc omega_ omaF fracsqrttimesR+sqrttimesR^+timesfracLCtimesL oma approx resultomaP omega_ ombF frac-sqrttimesR+sqrttimesR^+timesfracLCtimesL omb approx resultombP abcliste
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Exercise:
A RO resistor a LO inductor and a CO capacitor are connected in series to an ac voltage supply. abcliste abc Derive a formal expression for the angular frequency at which the impedance of an RLC series circuit is equal to twice the resistance: ZomegaR. abc Calculate the numerical value of the angular frequency in a. abcliste

Solution:
abcliste abc The condition can be written as Zomega sqrtR^+leftomega L-fracomega Cright^ R Longrightarrow R^+leftomega L-fracomega Cright^ R^ Longrightarrow omega L-fracomega C pm sqrt R This leads to the quadratic omega^ L mp omega sqrt R-fracC with the positive solutions omega_ fracpmsqrtR+sqrt R^+dfracLC L abc omega_ omaF fracsqrttimesR+sqrttimesR^+timesfracLCtimesL oma approx resultomaP omega_ ombF frac-sqrttimesR+sqrttimesR^+timesfracLCtimesL omb approx resultombP abcliste
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Circuits
Tags
ac circuit, impedance, rlc series circuit
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Difficulty
(3, default)
Points
0 (default)
Language
ENG (English)
Type
Calculative / Quantity
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