The graph of frequency vs V in /V out (high pass and low pass filter) should alw
ID: 1973733 • Letter: T
Question
The graph of frequency vs Vin/Vout (high pass and low pass filter) should always cross at the frequency where Xc (capacitance reactance) = R (resistance). Why is this?
Additional information:
An RC circuit can be used as a filter. The signal generator voltage is your input voltage, Vin. If you measure the output voltage, Vout, across the resistor you will have a high pass filter since at high frequencies the voltage will be larger. If you measure Vout across the capacitor you will have a low pass filter since at low frequencies the voltage will be larger.
Xc= 1/2fC
The generator voltage will not be in phase with either of the voltages. It will differ from the current by a phase angle where: tan(phase) = -Xc / R
the total resistance of the circuit is replaced by the impedance, Z.
Z= sqrt(Xc^2 + R^2)
Explanation / Answer
Lets see the transfer function of both of the high pas ans low pass filters high pass=R*sc/(1+scR) low pass=1/(1+sc*R) now lets find the frequency where they both are equal ==>R*sc=1 (cancelled the denominators) ==>s=1/R*c at this frequency Xc=1/sc=R so at this frequency we have R=Xc It can be logically xplained like this high pass filter passes all the frequencies starting from the point where potential difference across R and C is equal and low pass passes frequencies upto the point where where potential difference across R and C are equal
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