Exercise
https://texercises.com/exercise/rlc-series-circuit-1/
Question
Solution
Short
Video
\(\LaTeX\)
No explanation / solution video to this exercise has yet been created.

Visit our YouTube-Channel to see solutions to other exercises.
Don't forget to subscribe to our channel, like the videos and leave comments!
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
Report An Error
You are on texercises.com.
reCaptcha will only work on our main-domain \(\TeX\)ercises.com!
Meta Information
\(\LaTeX\)-Code
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
Contained in these collections
  1. 3 | 18
  2. 17 | 29

Similar exercises (19)
Title Matched on
Maximum and Asymptotic Behaviour of Parallel Impedance tags
Partial Voltages in RC Circuit tags
Partial Currents in Parallel Circuit tags
Tone Control tags
Impedance tags
more (14 more)
Attributes & Decorations
Branches
Circuits
Tags
ac circuit, impedance
Difficulty
(3, default)
Points
0 (default)
Language
ENG (English)
Type
Calculative / Quantity
Decoration
Content image