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March 27, 2017

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I have to calculate the voltage across the resistor of an rlc circuit where the 4.7nF capacitor is in parallel with the .200 H inductor for different frequencies (starting with 1000 Hz) They appear at the top of the circuit and they both looked to be in series with the 5100 ohms resistor. The source voltage is 5 volts.

I don't really know how to do the calculations for this one since I know in a parallel one all of them will have the same voltage I had to calculate Vr for a series rlc cricuit and I used the voltage divider rule.
Vr=vs*R/sqrt(R^2+Xt^2)
where
Xt=Xl-Xc
xt=wL-(1/wc)
and calculated resonant frequency using:
fr=1/(2*pi*sqrt(LC))

I used the same equation for fr for the series parallel one. How can the voltage vr be calculated for the series parallel circuit? Can the same method be used?

When calculating bandwidth and quality factor will the series be considered parallel?

  • Circuits - ,

    F = 1000 Hz.
    L = 0.200H.
    C = 4.7 nF = 4.7*10^-9 Farads.
    R = 5.1 k Ohms.

    Xl = 2pi*F*L = 6.28*1000*0.20 = 1,256 Ohms.
    Xc = 1/(2pi*F*C).
    Xc = 1/(6.28*1000*4.7*10^-9) = 33,880 Ohms.

    Z = Xl*Xc/(Xl+Xc).
    Z=(1256*-33,880)/(1256-33880)=1304.4
    Ohms = Impedance of parallel circuit.

    Zt = R + jX.
    Zt=5100 + j1304.4=5264.2 Ohms @14.35 Deg. = Total impedance.

    I = E/Zt = 5 / 5264.2=9.5*10^-4 Amps.

    Vr = I*R=9.5*10^-4 * 5100=4.85 Volts

    Repeat the procedure for all required frequencies.

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