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Exercise:
A RO resistor and a CO capacitor are connected in series to an ac voltage with amplitude VO. abcliste abc Calculate the partial voltages across the resistor and across the capacitor for a frequency of fO. Why is the of the two partial voltages not equal to the total voltage? abc Calculate the frequency for which the partial voltage across the capacitor is half the input voltage. abcliste

Solution:
abcliste abc The current through both the resistor and capacitor in series is I fracV_Z fracV_sqrtR^+fracomega C^ The partial voltage across the resistor is V_R R I V_fracRsqrtR^+fracomega C^ VRF Vtimesfracsqrt+fracpitimesftimesRtimesC^ VR approx resultVRP The partial voltage across the capacitor is V_C X_C I V_fracomega CfracsqrtR^+fracomega C^ VCF labelvcap fracVsqrtpitimesftimesRtimesC^+ VC approx resultVCP The two partial voltages are not in phase but have a phase shift of pi/. The total voltage is equal to V_ VtotF sqrtVR^+VC^ VtotP as expected. abc For the voltage across the capacitor to be one half of the input voltage we have the following condition see refvcap: V_C VCF fracV_ It follows that pi f RC^+ pi f RC sqrt and finally for the frequency f fhF fh approx resultfhP abcliste
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Exercise:
A RO resistor and a CO capacitor are connected in series to an ac voltage with amplitude VO. abcliste abc Calculate the partial voltages across the resistor and across the capacitor for a frequency of fO. Why is the of the two partial voltages not equal to the total voltage? abc Calculate the frequency for which the partial voltage across the capacitor is half the input voltage. abcliste

Solution:
abcliste abc The current through both the resistor and capacitor in series is I fracV_Z fracV_sqrtR^+fracomega C^ The partial voltage across the resistor is V_R R I V_fracRsqrtR^+fracomega C^ VRF Vtimesfracsqrt+fracpitimesftimesRtimesC^ VR approx resultVRP The partial voltage across the capacitor is V_C X_C I V_fracomega CfracsqrtR^+fracomega C^ VCF labelvcap fracVsqrtpitimesftimesRtimesC^+ VC approx resultVCP The two partial voltages are not in phase but have a phase shift of pi/. The total voltage is equal to V_ VtotF sqrtVR^+VC^ VtotP as expected. abc For the voltage across the capacitor to be one half of the input voltage we have the following condition see refvcap: V_C VCF fracV_ It follows that pi f RC^+ pi f RC sqrt and finally for the frequency f fhF fh approx resultfhP abcliste
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Attributes & Decorations
Branches
Circuits
Tags
ac circuit, impedance
Difficulty
(3, default)
Points
0 (default)
Language
ENG (English)
Type
Calculative / Quantity
Decoration
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