4.133. /0// = -V1 (Q 2 + 1/4) (12 — 1)2 /12, 2.2 and 19 respectively.
4.134. t = i/zato.
4.135. (a) I = —Io z 1.154; (b) I = Y8 Io 1.1110R
4.136.
2/tL,
1= 2 kHz.
4.137. The current lags behind the voltage by the phase angle
(IDarccos
P= - 1;1/ Z2 - Xi = 0.16 kW.
172
4.138. For R=
0.20 k52; P „ „ =
--= 0.11 kW.
20)L
4.139. Increased by
30%.
4.140. For Q >> 1 the ratio is A0)/(60 1/21/ — 1/Q = 0.5%.
IR
Axis of
Ic
Axis of
IR Axis of
es
g
lt
voltages
voltages
voltages
\
10
\
I
-- IO
IL
Iv
I Lx
IL
(a)
(6)
(c)
Fig. 32.
4.141. P2 = 112 (V2 — 1/ — VDIR = 30 W.
4.142. P1 = 1/2 (1 2 —
— R
2.5 W.
4.143. Z = R/1/1 (o)CR)2 = 40 O.
4.144. See Fig. 32.
4.145. (a) w,es
=
LC
3 .104 rad/s; (b) / = VRC/L =-.
=3 mA, /L = V VCIL = 1.0 A, /c = V 17T C: —
) 2 = 1.0 A.
4.146. tan cp —
(t)C (R2+ co2L2)— "
•
4.147. Z=
R2 ± cu2L2
(0)cR)2+ (1— w2CL)2•
oi2L2Li2/3 8L12
4.149. (Fx)= 2 (R2 + OLD ox •
2/
4.150. t =
a (VT+ liT2)
4.151. Acp =1 I (x1 — x2) cos a +
Y2) cos 0+(z1-z2) cos
4.152. k=w v1
V2
V3
4.153. t = a cos [(1 — V/v) cot — kx1 ], where v = (o/k.
4.155. (a) a/X, = 5.1 .10-5; (b) v,„ = 11 cm/s, 3.2.10 -4;
(c) (at/ax),,, = 3.2.10 -4, (avat),,,---1, (alai),,,, where v = 0.34 km/s
is the velocity of the wave.
330