A series RC circuit is often used a s a high-pass filter. Consider a resistor R

Question

A series RC circuit is often used a s a high-pass filter. Consider a resistor R and capacitor C connected in series to an oscillating source of emf with amplitude epsilon max. In terms of epsilon max, what is the amplitude of the voltage across the resistor for a low frequency, when RC = 1/2.0 times 10 ? epsilon R,max = For a high frequency, when RC = 2.0 times 10 ? epsilon R,max = At what frequency is the amplitude of the voltage across the resistor equal to epsilon / (2)0.5? Write your answer in terms of the resistance R and the capacitance C.

Explanation / Answer

a) The voltage across the resistor is given by voltage divider rule as

Er = Emax * (R/ [ R+1/jwC ] )

Er = Emax * jwCR/(1+jwCR)

I am not ablse to guess whatis the power in the expression assuming it is 1

wCR = 1/20

Er = Emax * j0.05/(1+j0.05)

which comes to be very less so 0

b)

Er = Emax * jwCR/(1+jwCR)

I am not ablse to guess whatis the power in the expression assuming it is 1

wCR = 20

Er = Emax * j20/(1+j20) = Emax * 20ang(90) / 20ang(87.137)

= Emax * 1ang(2.87) = Emax(0.998 + j 0.05) Emax

c) Er = Emax * jwCR/(1+jwCR)

Emax/2 = Emax * 1/( 1/jwCR + 1 )

1/jwCR + 1 = 2

1/jwCR = 0.414

>>> w = 2.414/CR

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