Passive RC Circuit Natural Response Lab

Passive RC Circuit Natural Response Lab

Overview: In this lab, we experimentally examined the natural response of a simple RC circuit. We recorded the difference in circuit response between a manual switching on-and-off of a constant voltage, and the oscillating effect of a square wave voltage input. 

Design: We designed the following circuits:

^^^^ Circuit A: Circuit with a manual switch^^^^

^^^^ Circuit B: Circuit with a square wave^^^^

C= 22 microFarads

R1= 1K ohms

R2= 2.2K ohms

Expected circuit responses:

Circuit A)

Time constant = R2*C = 2200*(22*10^-6) = 48.4*10^-3

Vc(t)=Vc(0)e^(-t/Tau)

<=>

t=-Tau*ln(Vc(t)/Vc(0)) => -(48.4*10^-3) * ln(.01/5) = 300 ms

Circuit B)

Time constant = ((R2*R1)/(R2+R1))*C = ((2200*1000)/(2200+1000))*(22*10^-6) = 12.8*10^-3

Vc(t)=Vc(0)e^(-t/Tau)

<=>

t=-Tau*ln(Vc(t)/Vc(0)) => -(12.8*10^-3) * ln(.01/5) = 79.5 ms

Construction and Execution:

R1 was measured at .998K ohms

R2 was measured at 2.15K ohms

C was measured at 19.05 microFarads

Results:

^^^^ Results from Circuit A ^^^^

Time required to get to .01V = ~80 ms.

^^^^ Results from Circuit B ^^^^

Time required to get to .01V = ~80 ms.

Analysis: Based on our results quite a few things are apparent. Number 1: Circuit B behaved just as expected, and the method of execution/prediction was perfect. This is confirmed by the fact that its response time was equal to the predicted response time by +/- 4.9%. Number 2: Circuit A was predicted to behave differently than it did. Simply turning off the power supply doesn't actually disconnect the power supply from the circuit, it simply behaves as a short. This caused R1 to still be involved in the circuit, and drastically reduce the amount of time necessary to discharge the capacitor. This is made clear by the fact that the circuit responded to within +/- 1.9% of Circuit B's predicted response, and +/- 277% of Circuit A's predicted response. The answer is clear. In order to redo Circuit A properly, a physical switch must actually be implemented.