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?
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.
To calculate the voltage across the resistor (Vr) in the series-parallel RLC circuit, you can still use the voltage divider rule. However, since you have a combination of series and parallel elements, the impedance values need to be calculated differently.
First, let's calculate the impedance of the inductor (XL) and the capacitor (XC) using the formulas:
XL = 2πfL
XC = 1 / (2πfC)
where f is the frequency in Hz, L is the inductance in Henrys, and C is the capacitance in Farads.
Next, calculate the total impedance (Zt) by finding the sum of the resistive (R) and reactive (Xt = XL - XC) components:
Zt = R + Xt
Now you can use the voltage divider rule to find Vr:
Vr = Vs * (R / Zt)
where Vs is the source voltage.
As for the resonance frequency (fr), it can be calculated using the formula you mentioned:
fr = 1 / (2π * √(LC))
In the case of bandwidth and quality factor calculations, you will consider the circuit as a series RLC circuit since the resistor, inductor, and capacitor are connected in series. The parallel element only affects the overall impedance, but for those calculations, you will work with the series values.
I hope this explanation helps you in calculating the voltage and understanding the series-parallel RLC circuit.