Series RLC - calculate V w/ different ƒ

In summary, an L-C series RLC filter with a 2700 Ω resistor and a 5 V supply can pass frequencies between 5 and 10 kHz, but attenuates frequencies higher than 10 kHz by 25%.
  • #1
dwn
165
2

Homework Statement


Series RLC - Band Pass Filter[/B]
R = 2700Ω
Vi = 5 Vpp
C = 10 nF
L = 33 mH
I need to find the voltage across the resistor for different frequencies.

Homework Equations


w = 2pi*ƒ
V = R*Vi / (jwL + 1/jwC+R)

The Attempt at a Solution


This is from a lab experiment. How can I use the source voltage, R and ƒr to find the voltage across R at different frequencies.

-----update -----
sorry about that. new values added above.
 
Last edited:
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  • #2
dwn said:

Homework Statement


Series RLC - Band Pass Filter[/B]
R = 2700Ω
Vi = 5 Vpp
I need to find the voltage across the resistor for different frequencies.

Homework Equations


w = 2pi*ƒ
V = R*Vi / (jwL + 1/jwC+R)

The Attempt at a Solution


This is from a lab experiment. How can I use the source voltage, R and ƒr to find the voltage across R at different frequencies.
You haven't given all the information required: What are the values of L and C?
 
  • #3
Your relevant equations are indeed relevant. You've correctly written a voltage divider equation which will give you the voltage across the resistor for values of Vi and f. Of the the result will be a complex value. You might try reducing it to magnitude and angle (polar) form. In the lab, what device (test equipment) was used to read the output voltage?
 
  • #4
We used an oscilloscope to read the measured values, now I have to calculate the data with the given data for comparison. Then find the percentage error.
 
  • #5
dwn said:
We used an oscilloscope to read the measured values, now I have to calculate the data with the given data for comparison. Then find the percentage error.
Okay. So you'll have recorded values for the waveform peaks, thus the voltage magnitudes, for various frequencies. You can use your voltage divider equation to calculate the voltage and determine the theoretical magnitude values. Again, you might want to reduce the formula to a magnitude version.
 

FAQ: Series RLC - calculate V w/ different ƒ

1. How do I calculate the voltage in a series RLC circuit with different frequencies?

To calculate the voltage in a series RLC circuit with different frequencies, you will need to use the formula V = IZ, where V is the voltage, I is the current, and Z is the impedance. The impedance for a series RLC circuit is equal to the square root of the sum of the square of the resistance (R) and the reactance (X). The reactance is dependent on the frequency (f) and the capacitance (C) or inductance (L) of the circuit. Therefore, to calculate the voltage at different frequencies, you will need to adjust the reactance value accordingly and then plug the new impedance value into the V = IZ formula.

2. What is the difference between a series RLC circuit and a parallel RLC circuit?

A series RLC circuit consists of a resistor, inductor, and capacitor connected in a single loop, while a parallel RLC circuit has these components connected in separate branches. In a series RLC circuit, the current is the same throughout the circuit, whereas in a parallel RLC circuit, the voltage is the same across each branch. Additionally, the impedance in a series circuit is calculated by adding the individual impedance values, while in a parallel circuit, the inverse of the total impedance is calculated by adding the inverse of each individual impedance.

3. How does changing the frequency affect the voltage in a series RLC circuit?

Changing the frequency in a series RLC circuit affects the voltage by changing the reactance of the circuit. The reactance is inversely proportional to the frequency, meaning as the frequency increases, the reactance decreases, and vice versa. This change in reactance affects the overall impedance of the circuit, which in turn affects the voltage calculated using the V = IZ formula.

4. What is resonance in a series RLC circuit?

Resonance in a series RLC circuit occurs when the reactance of the inductor and capacitor cancel each other out, resulting in a minimum impedance and maximum current. This means that the voltage in the circuit will be at its maximum. At resonance, the frequency is equal to the resonant frequency, which is calculated by dividing the reciprocal of 2π by the product of the capacitance and inductance values.

5. How can I graph the voltage in a series RLC circuit with different frequencies?

To graph the voltage in a series RLC circuit with different frequencies, you will need to plot the voltage values calculated using the V = IZ formula at different frequencies. The x-axis should represent the frequency, while the y-axis represents the voltage. The resulting graph will be a curve with a peak at the resonant frequency. This can help visualize how the voltage changes with different frequencies in a series RLC circuit.

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