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1

 

1.    

 

: i1 i2

 

 

+ I(t)

R1 R2 U2

C

 

 

 

 

:

 

I(t)

R1

R2

C

2*(1-e-t/0,6*10 )1(t)

100

200

2000

 

 

:

 

 

I0=i1+i2

 

I2R2=I1R1+Uc

 

(I0-I1)R2= I1R1+Uc

 

I1(R1+R2)+Uc=I0R2

 

:

 

( (R1+R2)/R2)dUc/dt+Uc/R2=I(t)

 

:

 

( (R1+R2)/R2)p+1/R2=0

 

:

p=-1/(R1+R2)=-1/t

t t

Uc(t)=e-t/tò (I(t)1(t)*R2/ (R1+R2))et/t dt=(I0*R2/ (R1+R2))te-t/tòet/t dt =I0*R2e-t/tet/t ½ =

0 0

 

=I0*R2e-t/t[ et/t-1]= I0*R2 [1-e-t/t]

 

I1(t)=CdUc/dt=(IoCR21/t) e-t/t =(IoR2/(R1+R2)) e-t/t

 

I2(t)=Io[1-R2/(R1+R2)) e-t/t]

U2=I2*R2= Io[R2-(R22/(R1+R2)) e-t/t]

:

hI2=1-R2/(R1+R2)) e-t/t=1-0.67 e-t/t

 

hU2=R2[1-(R2/(R1+R2)) e-t/t]1(t) t=C(R1+R2)=0.6 10-6

 

hU2=200[1-0,67 e-t/t]1(t)

 

:

 

gI= R2/(R1+R2)2C)e-t/t+[1-R2/(R1+R2)) ]e-t/td(t)=1.1*106 e-t/t+0.33d(0)

gU2=d hU2/dt=(R2*R2/(R1+R2)t e-t/t)) 1(t)+ R2[1-(R2/(R1+R2)) e-t/t]d(t)

 

gU2=0,22*109e-t/t1(t)+66d(0)

 

 

 

 

 

2. :

:

I(t)=2*(1-e-t/0,610 )1(t)

 

hI2=1-(R2/(R1+R2)) e-t/t1(t)

t

I=I(0)hI2(t)+ ò I(y) hI2(t-y)dy

0

I(0)hI2(t)= 2*(1-e0/0,610 ) hU2=0

 

I(t)=(2/0.6 10-6) e-t/0.6 10

t

ò(2/0.6 10-6 )e-y/0.6 10[1-0,67 e-(t-y)/0.6 10]dy

0

t t

1) ò(2/0.6 10-6)e-y/0.6 10dy= -(0.6 10-62/0.6 10-6) e-y/0.6 10½=-2[e-t/0.6 10-1]= 2[1-e-t/0.6 10]

0                                                                                                                                                                                            0

 

t t

2) -(2*0,67/0.6 10-6 ) òe-y/0.6 10 ey/0.6 10 e-t/0.6 10dy=(2,23 106)e-t/0.6 10ò1dy=

0 0

=-2,23 106 te-t/0.6 10=-2,23 106 te-t/0.6 10

 

I(t)2=-2,23*106 te-t/0.6 10-2e-t/0.6 10+2=2-2,23*106*te-t/0.6 10-2e-t/0.6 10

 

U2= I(t)2*R2

 

:

U2(t)=400-446*106 te-t/0.6 10-400e-t/0.6 10

 

 

 

 

3. , :

 

(jw)=I/I= (U2/R2)/(U2/Z)= Z/ R2

Z=(R2(R1-j/wC))/((R1+R2)-j/wC)

 

(jw)=(R1-j/wC)/((R1+R2)-j/wC)=Ö(R12+(1/Cw)2)/ (((R1+R2))2+(1/wC)2) *

*e-jarctg(1/wCR1)+ jarctg(1/wC(R1+R2)) =

 

=Ö((R1w)2+(1/C)2)/ ((R1+R2)w)2+(1/C)2) *e-jarctg(1/wCR1)+ jarctg(1/wC(R1+R2)) =

 

(jw)=Ö(10000*w2+0,25 1018)/(90000*w2+0,25 1018) * e-jarctg(10/0,2w)+ jarctg(10/w0,6)

 

 

(w)=Ö(10000*w2+0,25 1018)/(90000*w2+0,25 1018)

 

 

(w)=-arctg(106/0,2w)+ arctg(106/w0,6)

 

 

 

 

 

 

 

 

 

 

 

2

 

 

 

1. : Q0, r

 

: R