Question

Determine the Capacitance in uF (micro-Farads) of the system below using the data, graph and tolerance graph below.

R -ww G(s) 1/(RCs+1) ei R =1000 ohms 1 Slope T c(t) c() = 1 - e-(1/T B 0.632 Tolerance graph (Ts(2%) = 4*T): A A 4T 2T 3T 5T 63.2% 86.5% 95% 98.2% Of output 99.3% 0.75 0.5 Output curve: 0.25 0 0 0.025 0.05 0.075 0.1 0.125 Data: x(time) y(amplitude) 0.001 0.09516258196 0.002 0.1812692469 0.2591817793 0.003 0.329679954 0.004 0.3934693403 0.005 0.006 0.4511883639 0.5034146962 0.007 0.5506710359 0.008 0.009 0.5934303403 0.01 0.6321205588 0.011 0.6671289163 0.6988057881 0.012 0.013 0.727468207 0.014 0.7534030361 0.7768698399 0.015 0.016 0.798103482 0.017 0.8173164759 0.018 0.8347011118 0.019 0.8504313808 0.8646647168 0.02 0.021 0.8775435717 0.022 0.8891968416 0.023 0.8997411563 0.024 0.9092820467 0.9179150014 0.025 0014 0.9257264218 0.026 0.027 0.9327944873 0.028 0.9391899374 0.9449767799 0.029 0.03 0.9502129316 0.031 0.9549507976 0.032 0.959237796 0.033 0.9631168326 0.034 0.96662673 0.035 0.9698026166 0.9726762776 0.036 0.037 0.9752764735 0.038 0.9776292281 0.039 0.9797580886 0.04 0.9816843611 0.9834273246 0.041 0.9850044232 0.042 0.986431441 0.043 0.044 0.9877226601 0.045 0.9888910035 0.046 0.9899481643 0.047 0.9909047229 0.048 0.991770253 0.9925534169 0.049 0.05 0.993262053 0.051 0.9939032534 0.9944834356 0.052 0.9950084061 0.053 0.053 0.9950084061 0.9954834191 0.054 0.055 0.9959132286 0.9963021363 0.056 0.057 0.9966540345 0.058 0.9969724453 0.059 0.9972605552 0.06 0.9975212478 0.061 0.9977571323 0.062 0.9979705694 0.063 0.9981636952 0.9983384427 0.064 0.9984965608 0.065 0.998639632 0.066 0.067 0.9987690881 0.9988862249 0.068 0.9989922146 0.069 0.07 0.999088118 0.071 0.9991748951 0.072 0.9992534142 0.073 0.9993244612 0.9993887472 0.074 0.075 0.9994469156 0.076 0.9994995486 0.9995471728 0.077 0.078 0.999590265 0.9996292565 0.079 0.08 0.9996645374 0.9996964609 0.081 U.06 T 0.9996904609 0.082 0.9997253464 0.083 0.9997514832 0.9997751327 0.084 0.085 0.9997965316 0.086 0.9998158942 0.9998334142 0.087 0.088 0.9998492669 0.9998636111 0.089 0.9998765902 0.09 0.091 0.9998883342 0.092 0.9998989606 0.093 0.9999085758 0.094 0.9999172759 0.095 0.9999251482 0.096 0.9999322713 0.9999387165 0.097 0.098 0.9999445484 0.099 0.9999498253 0.1 0.9999546001 0.9999589204 0.101 0.9999628297 0.102 0.9999663669 0.103 0.104 0.9999695675 0.105 0.9999724636 0.106 0.999975084 0.9999774551 0.107 0.108 0.9999796005 0.109 0.9999815418 0.11 0.9999832983 0.111 0.9999848877 0.112 0.9999863258 0.9999876271 0.113 0.9999888045 0.114 0.9999898699 0.115 0.116 0.9999908339 0.9999917062 0.117 0.118 0.9999924954 0.119 0.9999932096 0.12 0.9999938558 0.121 0.9999944405 0.122 0.9999949695 0.9999954483 0.123 0.9999958814 0.124 0.125 0.9999962733 0.126 0.999996628 0.127 0.9999969489 0.128 0.9999972392 0.9999975019 0.129 0.13 0.9999977397 0.131 0.9999979548 0.132 0.9999981494 0.9999983255 0.133 0.134 0.9999984849 0.135 0.999998629 0.9999987595 0.136 0.9999988776 0.137 0.138 0.9999989844 0.139 0.999999081 0.14 0.9999991685

Answer 1

G(s) RC's1

step response

C(s) RC's1 S

RC C(s) RC's1

C(s) s(1/RC)

c(t) 1-et/RC

at t = 0.01 ; c(t) = 0.63212

0.63212 1-e-0.01/RC

0.01/RC0,36788

ne0.01/RC In(0.36788)

0.01/RC=I0.99999848

RC=0.01

Given R = 1000 ohms

$\Rightarrow 1000*C = 0.01$

C=105F

BC= 10F