342.sagews

# www.geocities.com/serienumerica4
# RC circuit 
# example 1rst order DE dq/dt +q/(R*C1)-Emf/R =0
t,R,C1,Emf = var('t,R,C1,Emf')    
q = function('q',t)   # defines q to be a function of that variable
DE = lambda q: diff(q,t) + q/(R*C1) - Emf/R
desolve(DE(q(t)), [q,t])

e^(-(t/(C1*R)))*(Emf*C1*e^(t/(C1*R)) + c)

t,y,q= var('t,y,q');
C1=1.E-6 ; Emf=6; R=1.E3;c=-C1*Emf;tau=R*C1;
q=exp(-(t/(C1*R)))*( Emf*C1*exp(t/(C1*R)) -C1*Emf )
#plot(exp(-(t/(C1*R)))*( Emf*C1*exp(t/(C1*R)) -C1*Emf ) ,t,0,3*tau).show
#(xmin=0,xmax=4*tau,ymin=0,ymax=6E-6)
#plot ((x^2+1),x,-2,2).show(xmin=-3,xmax=3,ymin=0.,ymax=6)
y=plot(q,t,0,3*tau)
#show(y)

#p = plot(sin,-pi,pi) 
#p.axes_labels(['foo','bar']) 
#p.show()

var('t');
C1=1.E-6 ; Emf=6; R=1.E3;c=-C1*Emf;tau=R*C1;
q=exp(-(t/(C1*R)))*( Emf*C1*exp(t/(C1*R)) -C1*Emf );
#p.axes_labels(['foo','bar']) 
#p.show() 
y= plot(q,0,3*tau)
y.axes_labels(['tsec','qcoul'])
show(y)

var('t');
q= exp(-(t/(C1*R)))*(Emf*C1*exp(t/(C1*R)) + -Emf*C1);
diff(q,t)

Emf/R - e^(-(t/(C1*R)))*(Emf*C1*e^(t/(C1*R)) - Emf*C1)/(C1*R)

C1=1.E-6 ; Emf=6; R=1.E3;c=-C1*Emf; tau=R*C1;
q=exp(-(t/(C1*R)))*( Emf*C1*exp(t/(C1*R)) -C1*Emf )
#var('xvar('t,q')
') 
#f=sin(x)+cos(x)*x^2
#fp=f.plot(xmin=0,xmax=10)
#fp.show()
qp=q.plot(xmin=0,xmax=3*tau)
qp.show()

var('x') 
f=sin(x)+cos(x)*x^2
fp=f.plot(xmin=0,xmax=10)
fp.show()

var('i,t')
C1=1.E-6 ; Emf=6; R=1.E3;c=-C1*Emf; tau=R*C1;
i=Emf/R - e^(-(t/(C1*R)))*(Emf*C1*e^(t/(C1*R)) - Emf*C1)/(C1*R);
ip=i.plot(xmin=0,xmax=3*tau);
ip.show()