For your final exam in electronics, you’re asked to build an LC circuit that oscillates at 10 kHz. In addition, the maximum current must be

Question

For your final exam in electronics, you’re asked to build an LC circuit that oscillates at 10 kHz. In addition, the maximum current must be 0.10 A and the maximum energy stored in the capacitor must be 1.0 x 10-5 J. What values of inductance and capacitance must you use?

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Nguyệt Ánh 4 years 2021-08-12T16:40:28+00:00 1 Answers 84 views 0

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  1. minhkhang
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    2021-08-12T16:41:39+00:00
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    Answer:

     L= 2 mH

    C=1.26\times 10^{-7}\ F            

    Explanation:

    Given that

    Frequency , f= 10 kHz

    Maximum current ,I = 0.1 A

    Maximum energy stored ,E= 1 x 10⁻⁵ J

    The maximum energy stored in the inductor is given as follows

    E=\dfrac{1}{2}LI^2

    Where ,L= Inductance

    I=Current

    E=Energy

    Now by putting the values in the above equation

    10^{-5}=\dfrac{1}{2}\times L\times 0.1^2

    L=\dfrac{2\times 10^{-5}}{0.1^2}\ H

    L=0.002 H

    L= 2 mH

    We know that frequency f is given as

    2\pi f=\dfrac{1}{\sqrt{LC}}

    C=Capacitance  , f=frequency ,L=Inductance

    Now by putting the values

    2\pi \times 10\times 10^3=\dfrac{1}{\sqrt{0.002\times C} }

    62831.85=\dfrac{1}{\sqrt{0.002\times C}}

    \sqrt{0.002\times C=\dfrac{1}{62831.85}

    0.002\times C=0.0000159^2

    C=\dfrac{0.0000159^2}{0.002}\ F

    C=1.26\times 10^{-7}\ F

    Therefore the inductance and capacitance will be 2 mH and 1.26 x 10⁻⁷ F respectively.

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