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Answer :
To achieve an output voltage of 3.97 V at a frequency of 57 Hz, given an input voltage of 29 V at the same frequency, the series RC circuit needs to have a specific combination of resistor and capacitor values.
In a low-pass filter circuit, the cutoff frequency determines the frequency at which the output voltage starts to decrease. To calculate the values for the RC circuit, we need to find the cutoff frequency and use it to determine the appropriate resistor and capacitor values. The cutoff frequency, denoted as fc, is the frequency at which the output voltage is reduced to [tex]\frac{1}{\sqrt{2}}[/tex] or approximately 0.707 times the input voltage. In this case, the cutoff frequency is 57 Hz, and the desired output voltage is 3.97 V. We can calculate the cutoff frequency as follows:
[tex]f_c = \frac{1}{(2 \times \pi \times RC)}[/tex]
To find the RC values, we rearrange the formula:
[tex]RC = \frac{1}{(2 \times \pi \timesf_c )}[/tex]
Substituting the values, we have:
[tex]RC = \frac{1}{(2 \times \pi \times 57 Hz)}[/tex]
Solving this equation will give us the required RC value. However, since you specified that the input voltage is 29 V, we need to consider the voltage division between the resistor and capacitor. The output voltage can be calculated using the voltage divider formula:
[tex]V_{out} = Vin \times (1 / \sqrt{(1 + (fc / f)^2))}[/tex]
Solving this equation for Vout = 3.97 V and Vin = 29 V, with the cutoff frequency fc = 57 Hz, will yield the resistor and capacitor values required for the series RC circuit.
To learn more about RC circuit refer:
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