Solutions

Circuits 3
complete the following problems from the book as well as the following problems'
Tipler Ch26:99, 100, 101, 102, 103' 104' 110' I I I
C=5pF
f= 3000 V
l. In the circuit shown above, i, un6#1i.'.u*.nts through resistors Rr andRz, respectively' vt' vz'
and v. are the potential difference, uilos resistor R1 resistor"R2, ord capacitor c, respectively' Initially the
capacitor is uncharged'
a. Calculate tf,. t,i*.nt i1 immediately after switch S is closed'
{=tg

Now the switch S is opened.
f. On the axes below, sketch the current i2 as a function of time t and clearly indicate initial and final
values.
,0'
U
cr4*Ft-i
s
r? = l00O
cz=r,stF Cu*os^s ts C*rry
er=L,{o
= 4^F{-)
eo= Zfll,C2 O,_rez
Z. Capacitors I and2,of capacitance C1 :4LrF and C2: l2pF, respectively, are connected in a circuit as
shown above with a resistor of resistance R: l00O and two switches. Capacitor I is initially charged to a
voltage Vo = 50 V, and capacitor 2 is initially uncharged. Both of the switches S are then closed at time t: 0.
a. What are the final charges on the positive plate of each of the,capacitors,l ayd2 after equilibrium has
been reached? \/
e,+ eo=eo
-L
vr =Vz Q, = S9 Q; Q"c'-
b. Determine the differenr. ffi-t *n.kt and the final store{ energy,of th; rrrt.Pui;ffimi* ^0"
,it5f',-r
u , = tr(4^ilb"u)'= fwor,
uF=t(Wry;=vm/^)
bv r.31 go,, )
c. Write, but do not solve, an equation that, at any time after the switches are closed, relates the charge on
capacitor C1, its time derivative (which is the instantaneous current in the circuit), and the parameters
Vo, R, C1, and C2. {, z OY,
Q; (, -r:e- V, ; - 61;- vo,, -e, !=-H'
-f='Z
Uz=
,J, * r *n-Y$,
_.. s' C, dpY- -
The current in the resistor is given as a function of time by I: Ioe-/', where Io:0.5A and t:3 x l0-as'
d o'ru";n:;" *,*:rgv dissipation
H'";"i'1; ]')t")t"::"
/= (T"
i '') Y-
":;
;*r
,r/du)
e. How much energy isn$issipated in the resistor from the instant the switch is closed to when equilibrium
isreachedt
\I= sr'*
of, -,_, -Ze/ry ?k/,v t .
t+
\'[= II'rze Cr'
At/ 'ry -r'
?. 31 fo,nr
L tJ
CL
wL