4.112. Q= ( 17) 17 - 1 6= = 1 .0 102.
4.113. (P) =R (I2)
112RA = 20 mW.
4.114. (P) = 1i2RCV,%/L = 5 mW.
4.115. w= /V LC 4R2C2 '
R <- /- .
4.116.-A-- — and — — = R
—
L,
L2
L
R2
•
4.117. I= V° te-t/V7-7c. I—I max 1 . e
—17 c- at the moment
'
t,n =1/17.
4.118. I—
Vrn
[cos (cot — cp)—cos cp • e-tR/L], tan cp = coL/R.
iiR2H-co2L2
4.119. I=
vm
[cos (wt
cos cp • e-t/RC],
tan cp =
1R2+1/((0C)2
-
coRC
4.120. The current lags behind
1
UcR
the voltage by phase angle cp, defined
Axis
I Axis
—L _ _
by the equation tan cp = 1A° 4n np 2'va
SRO
of current
I of current
4.121. The current is ahead of
(a)
r
the voltage by the phase angle
(b)
= 60°, defined by the equation
Fig. 31.
tan cp = (17,„/R/ni)2 —1.
4.122. (a) V' =Vo -i-V,,cos(cot— a), where Vm =170/V- 1 (coRC)2 t
= arctan (WIC); (b) RC =V 12 -1/co= 22 ms.
4.123. See Fig. 31.
4.124. (a)
= 17,n/YR2 + (coL —1/coC)2 = 4.5 A; (b) tan cp
,cp = — 60° (the current is ahead of the voltage);
(c) Vc - -= /,,,/coC= 0.65 kV, V L = 4,11R2 + co 2L2 0.50 kV.
4.125. (a) co = ci4 — 2f32; (b) w -= coVV co2 ,, — 2P2, where co: =
= 1/LC, 13 = RI2L.
4.126. For C =
= 28 iiF; V L = Vin
(coL/R)2 = 0.54 kV;
Vc = VnicoLIR= 0.51 kV.
vrn
4.127. I =In, cos (cot + cp), where
R
(coRC)2 and
tan cp = coRC.
L2
4.128. coo =
c (L1L2_ 14.2)
4.129. Q=V12 2 — 1/4.
rig -1
1
4.130. Q= 17 (n— 1)2
4 •
4.131. (a) coo = V 6)0)2; (b) Q=1/
0)1(02 (n 2 —
1
((02 —04)2
4 •
329