Please show work Suppose that an electric circuit contains a capacitor with capa
ID: 3080365 • Letter: P
Question
Please show work
Suppose that an electric circuit contains a capacitor with capacitance C = 5 * 10-6 farads and a resistor resistance of 1000 Ohm , in series. If a 200-volt electromotive force is applied to this RC-circuit during 10 minutes, find the charge q(t) on the capacitor after 10 minutes(approximately) assuming that initially q(0) = ). Hint: Use CR-series equation Rdq/dt + q/C = E(t). It is also convenient to use the Heaviside function H(t) =Explanation / Answer
rdq/dt+q/c=e..................=>rdq/dt=e-q/c..............=>dq/(e-q/c)=dt/r..... integrating on both sides we get..... -c*ln(e-q/c)=t/r+K where K is constant. q(0)=0 substituting t=0 and q=0 we get K as K=-c*lne. so the equation becomes -c(ln(e-q/c)/e)=t/r................................... =>q=ec(1-e^(-t/rc)).now substituting e=220,t=10*60=600sec,r=1000ohm,c=5*10^-6*96500 we get q=220*5*10^-6*96500(1-0.288)=75.54 coulumbs