A 10.5- resistor, a 15.9-μF capacitor, and a 15.2-mH inductor are connected in series with a 203-V generator. (a) At what frequency is the

Question

A 10.5- resistor, a 15.9-μF capacitor, and a 15.2-mH inductor are connected in series with a 203-V generator. (a) At what frequency is the current a maximum? (b) What is the maximum value of the rms current? Note: The ac current and voltage are rms values and power is an average value unless indicated otherwise.

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RobertKer 5 years 2021-08-02T20:54:53+00:00 1 Answers 12 views 0

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  1. ngochoa
    0
    2021-08-02T20:56:34+00:00
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    Answer:

    (a) Frequency at which current is maximum is 323.9 Hz

    (B) Maximum current in the circuit is 19.333 A

    Explanation:

    We have given resistance R = 10.5 ohm

    Capacitance C=15.9\mu F=15.9\times 10^{-6}F

    Inductance L=15.2mH=15.2\times 10^{-3}H

    (a) Current is maximum when impedance will be minimum and impedance is minimum when there is condition of resonance.

    At resonance X_C=X_L

    \frac{1}{\omega C}=\omega L

    \omega ^2=\frac{1}{15.9\times 10^{-6}\times 15.2\times 10^{-3}}

    \omega =2034.13

    2\pi f =2034.13

    f = 323.9 Hz

    (b) Current will maximum when resonance occurs at resonance impedance of the circuit is equal to resistance.

    Voltage is given V = 203 volt

    So maximum current i=\frac{203}{10.5}=19.333A

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