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Exercise:
The impedance of a circuit with a CO capacitor and a LO inductor connected in series to a voltage signal with amplitude VO and frequency fO is measured to be ZO. Calculate the circuit's resistance and the amplitudes of the voltage signals across the capacitor and the inductor.

Solution:
The impedance of an ac series circuit is given by Z sqrtR^+leftomega L-fracomega Cright^ Solving for the resistance leads to R RF sqrtZ^-leftpitimesftimesL-fracpitimesftimesCright^ R approx resultRP The partial voltage across the capacitor is V_C X_C I_ fracpi f CfracV_Z VCF fracVpitimesftimesCtimesZ VC approx resultVCP The partial voltage across the inductor is V_L X_L I_ VLF pitimesftimesLfracVZ VL approx resultVLP Both partial voltages are greater than the applied voltage. This is possible since the phasors for the partial voltages are in em antiphase i.e. the phase shift between them is pi/ and they partially cancel each other.
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Exercise:
The impedance of a circuit with a CO capacitor and a LO inductor connected in series to a voltage signal with amplitude VO and frequency fO is measured to be ZO. Calculate the circuit's resistance and the amplitudes of the voltage signals across the capacitor and the inductor.

Solution:
The impedance of an ac series circuit is given by Z sqrtR^+leftomega L-fracomega Cright^ Solving for the resistance leads to R RF sqrtZ^-leftpitimesftimesL-fracpitimesftimesCright^ R approx resultRP The partial voltage across the capacitor is V_C X_C I_ fracpi f CfracV_Z VCF fracVpitimesftimesCtimesZ VC approx resultVCP The partial voltage across the inductor is V_L X_L I_ VLF pitimesftimesLfracVZ VL approx resultVLP Both partial voltages are greater than the applied voltage. This is possible since the phasors for the partial voltages are in em antiphase i.e. the phase shift between them is pi/ and they partially cancel each other.
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Circuits
Tags
ac ciruit, ac series circuit, impedance, partial voltage
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Difficulty
(2, default)
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0 (default)
Language
ENG (English)
Type
Calculative / Quantity
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