3.169. (a) 11 1 = 23-ca/S 2 ; (b) E 231a//S 2.
3.170. t = -RC In (I - VIVO = 0.6 tis.
3.171. p = %leo In 2 = 1.4.10 13 5 - 2•m.
3.172. I = [(11 - 1) g 1 I1] e-rit/RC.
3.173. V = + 1) = 2.0 V.3.174. (pi - = (el - + R 2 ) - e, = -4 V.
3.175. R = R2 - R 1 , Acp = 0 in the source of current with in-
ternal resistance R^2.
3.176. (a) I = a; (b) CPA - tP B = 0.3. 177. PA - B = (el - R1/(R1 + R2) = -0.5 V.
3.178. / 1 = eR 2 /(RR^1 RiR 2 R^2 R) = 1.2 A, 12 = 1 1R1/R2=
= 0.8 A.
3.179. V = V oRx1ER1 R (1 - x) x111; for R > Ro V
V ox11.
3.180. t = (g 1R 2 g2R1)/(Ri + R2), Ri = R^1 R^2 /(R^1 + R2).
3.181. I = (R 162 - R261)1(RR1 R1R2+ R^2 R) = 0.02 A, the
current is directed from the left to the right (see Fig. 3.44).
3.182. (a) (^) = [R3 (et - + Rol + gov(R,R, + R2R3 +
+ R 3 R 1 ) = 0.06 A; (b) (pA -cpB = gi 101 = 0.9 V.
3.183. I = [6 (R 2 + R3) + 0 R 3 ]1[11 (R (^2) + R3) + R2R3].
3.184. TA.- (I) B = [e2R3 (R1 + R2) - g1R1 (R2 +R 3 )11(14112+
▪ R 2 R 3 R3R1) =- -1.0 V.
3.185. / (^1) = [R3 ((Pi - (1)2) - 4 - R2 (Cl (P3)1 (^1) (R1R2 R2R3
▪ R3R1) = 0.2 A.
3.186. I= Ri+R2^
R2 ( R1 [I ± R2R4 (R1+ R3) /RIR 3 ( (^11) 2 R4)]
- = 1.0 A.
The current flows from point C to point D.
3.187. R AB = r (r 3R)1(R 3r).
3.188. V = 1/^2 e (1^ e-2tniC).^
3.189. (a) Q = 4 /3 q^2 R1 At; (b) Q =^1 /2 In 2.q^2 R/At.
3.190. R = 3R 0.
3.192. Q I (g - v) = 0.6 W, P = -IV =-2.0 W.
3.193. I = V12R; Pmax = V 2 /4R; 1 1 = 1/2.
3.194. By 2i = 2%.
3.195. T - To = (1 - e-htic) V 2 /kR.
3.196. R x = + R 2 ) = 12 52.
3.197. R = R1R 2 I(R1 + R2);
Qyna. = (e1R2 + F 2 111) 2 14R1R2 (R1 + R2).
3.198. n 111 n TrIR =3.
3.199. Q =^112 C6 (^2) 1111(R1 + R 2 ) = 60 mJ.
3.200. (a) AW = - 1 / 2 CV 2 i/(1 1) = -0.15 mJ; (b) A
= 11 2CV 2111 (^1 - 11) = 0.15 mJ.
3.201. AW = - 1 / (a - 1) 2 CV^2 = -0.5 mJ,^ A rnech
= 1 /2 (a - 1) Cr 0.5 mJ.
3.202. h 1 / 2 a 0 (a - 1) V^2 /pgd^2 , where p is the density of water.
3.203. (a) q = qoe-1/80 6 P; (b) Q = (1/a - 1/b) Oneo e.
3.204. (a) q = qo (1 - e-t/RC) = 0.18 mC; (b) Q
= (1 - e - Inic)q/2C = 82 mJ.