Cutoff frequence of a capacitor // resistor

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Can anyone prove that the cutoff frequence of a capacitor // resistor ?
 

I find your question kind of vague. What are you asking? Please paraphrase your question.
 

like a filter RC low pass, that the cut off frequencie is fc=1/2piRC.
Look likes that the cutoff freq of R//C is the same, but can't desenvolve it.
 

In other to solve a circuit RC, RLC, series or parallel you have first to work with the differential equation, pass to laplace domain and after you have to analyze the poles and zeroes of the system . With the help of bode diagram you can easily visualize the magnitude and phase x frequency and consequently determine the cutoff frequency.

You can jump the differential equation step using the Laplace representation of Resistors , Capacitors and Inductor and get the transfer function through simple circuit analysis.
 

Z=R // C

Z= (R*1/Cwj ) / (R + 1/Cwj) =R/(1+RCwj)

magnitude(Z)=R/√(1+(RCw)²)

so cut off is the frequency at which response is 1/√2 times the maximum value

max value=R for w=0

R/√(1+(RCw)²)=max/√2=R/√2

=> RCw=1 and w=1/RC
 

I may think that your question is not quite clear. The well known cutoff frequency can be found in the topic of 'Photoelectric effect'. While the cutoff frequency of a capacitor// resistor may possibly refer to the resonant frequency of the RC circuit. If it is right, then you may find the answer from any physics book, like Physics, James Walker, 2nd edition, Pearson publishing company. Feel free to contact me should you have any queries. Thank you for your time to look at this message.
 

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