egee 203l - experiment 5 chris

8/16/2019 EGEE 203L - Experiment 5 Chris

1/12

Experiment 5

Transients in RC Circuits

Introduction

The purpose of this experiment is to study the transient response of simple RC

circuits to step-function excitation. In our first circuit, the time constant will be so long

that we will be able to study and obsere the behaior using meters. !sing the second

circuit we will hae a much shorter time constant resulting in us haing to use the

oscilloscope to ma"e the obseration and study. In order for us to get a large time

constant we need large resistors and large capacitors. The problem here is that the

insulation in these electrolytic capacitors is not of ery high #uality and current will still

flow through it. $ith a short time constant we can use our decade capacitor boxes since

they are of high #uality and their lea"age of resistance is basically negligible.

%urthermore, we had to calculate &i' and &'. Then we would graph these alues and get a


2/12

logarithmic plot of the experimental data. (astly, we would use the oscilloscope to s"etch

)C and )R .

*rocedure

+. et up the circuit shown below, %igure +, with C 5 μF and ) /5 ).

%igure +

/. Connect a wire from one terminal of the capacitor to the other and then remoe it

to discharge the capacitor.0. Close the circuit and read the current eery + seconds for approximately the first

three time constants of the circuit. $ait another 1 or 5 time constants and record if .1. %ind the theoretical time constant using the nominal alues of the components.


3/12

5. 2etermine the actual time constant of the circuit using the method described in

*art II.3.1.4. 2etermine the actual alues of C and R p.

. tudy the difference between the circuit aboe and the circuit below, %igure /.

%igure /

6. Change the circuit to %igure / without discharging C and read &' eery +

seconds for approximately the first 0 time constants using the impson /4.

7. Then use &' to find &i', using the internal resistance of the impson meter.+. !sing the alues found in *art III.3.4 determine the theoretical alue of the new

time constant.++. !sing the alues found in *art II.8.0 determine the new time constant and

compare it with the theoretical alue.+/. et up the circuit shown below, %igure 0, and set the fre#uency to + 9:, R

+ ohms, C ./ μF , ) + ). et the oscilloscope to obsere ) and )C.

%igure 0

+0. "etch )C to scale for C .+, .0, .+, .0, and +. μF .+1. et the oscilloscope to obsere )R ) ; )C, and s"etch )R to scale for the same

alues of C.


4/12

Results

V = IR

R=V

I

¿ 22.5V

50 x10−6

A

R=450,000Ω=450k Ω

3.+.

τ = RC

¿450 kΩ (50 μF )

τ =22500ms=22.5 s

3./.,3.0.

3 τ =3 (22.5 )=67 s

τ (s) i ( μA )+ 05

/ /0

0 +5

1 +.5

5

4 5

0.5

++ .5

Table +

3.5.

τ = 20−10

ln i(35

21)=23.82 s


5/12

0 20 40 60 80 100 120

-0.5

0

0.5

1

1.5

2

Time vs Log of Current

Time(s)

Log i(t) (micro-amps)

%igure 1> Time s (og of Current

3.4.

if = V s

R+ R p

R p=V

it − R

¿ 22.5V 0.5 μA −450k Ω

R p=44.66 M Ω

C = R+ R p R R p

τ

C =53.17 μF

*art 8>

8.+.,8./.

τ (s) V


6/12

1 +/ +/

5 + +

4 6 6

4.5 4.5

Table /

8.0.

τ =49.40 s

8.1.

20.5

17

ln i(¿)=53.41 s

τ =20−10

¿

0 10 20 30 40 50 60 70 80

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Time vs Log of Current

Time (s)

Log i(t) (micro-amps )

%igure 5> Time s (og of Current

*art C>


7/12

%igure 4> )C for C .+ μF

%igure > )R for C .+ μF


8/12

%igure 6> )C for C .0 μF

%igure 7> )R for C .0 μF


9/12

%igure +> )C for C .+ μF

%igure ++> )R for C .+ μF


10/12


11/12

%igure +1> )C for C +. μF

%igure +5> )R for C +. μF


12/12

2iscussion of Results and Conclusion

The purpose of this experiment was to study the transient response of simple RC

circuits to step-function excitation. %irst we needed to find out time constant and

determine our current with a capacitor in our circuit. This capacitor essentially caused our

current to drop exponentially relatie to time. $hen comparing both graphs to the

theoretical alues we notices that the graphs' alues had a slightly higher percentage error

due to human errors. The drop in current at 5 μA was much larger than that of the

drop in ) at /5). This essentially reflects that the electric conductance is higher. The

s"etches of the oscilloscope in *art C show )C and )R . %rom the oscilloscope we can

determine that with a higher alue of conductance, the waeforms for both oltages are

less of a sinusoidal wae, but more of s#uare periodic wae.

egee 203l - experiment 5 chris

Documents