Question

this is a question from a review for a test. please help!

An RC circuit with R = 10 Kilo-ohms and C = 40 nano-Farads is constructed to serve as an example of a first order system and as a filter. The capacitor is uncharged when the circuit is assembled. Two sources of input voltage to the circuit are possible, a DC power supply or a function generator. 1a) (6 points) • What input source would be used to determine the time response of this RC circuit to a step input, Vin = 5 volts? • Describe how you would use this source to generate a step input. 1b) (7 points) What is the time constant, tau, of the RC circuit? Sketch the time response of the circuit. At what time value will the voltage across the capacitor reach approximately 99% of the applied input voltage? 1c) (6 points) • What source would be used to determine the frequency response of the RC circuit? • Describe how you would use this source to excite the circuit. 1d) (6 points) What is the cutoff frequency of the circuit, in Hz? What is the magnitude value of the filtered signal at the cutoff frequency? Sketch the Gain of the circuit (Vfiltered/Vin) as a function of frequency, if this is acting as a low-pass filter

Answer 1

lok Given circuit is yong A step input of short duration, which is a Cpulse can be given to find the time response of the circuit ie de signal must be given u(t-2)-u(6-4) Exa ult) >t dc 10 2 4 • DC source of some reduced magnitude must be applied such that voltage across the capacitor doesn't break it's strength so for this R anda must be connected in series. 5V + 400F Vect) Time constant T = RC = lokx non 400 u sec 4x10 sec ooymsec I
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Velt) sy >t 5(lete) e - tovxo») sli-e -(i-e2500+) ; +20 Vc (t) 0.99(5) 0.9915) = 15 (i-e -2500+) - 2 soot e 0:0) 25oot e 100 > 2500 t = balloo) = 4.605 t= 1.842 msec Ac source with frequency range con be applied to find the frequency response : Resistance M R = Vs X = عليا Nm sinut

1 Rc 2 Soo d cut off frequency w f ZTRC 21 xlokx40x169 6 ५००x210 = 397.88 HZ Vo (5) Vics) ) FR + RSC Sc 1 + S (ouxios) Vo(s) 2500. S + 2 500 (vo(a) = 2.500 SW²+25002 25oo -14 √2500² +2500? √2 The magnitude at cut off frequeny = 1/2 I vocal Vils) n zolog (2500) 67.4503 - 67-95 2500 sw Grain us frequency yes. It acts as Low pass filter LPF