3.169. (a) 111 = 23-ca/S2; (b) E
231a//S2.
3.170. t = -RC In (I - VIVO = 0.6 tis.
3.171. p = %leo In 2 = 1.4.1013 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 -
+ R2) - e, = -4 V.
3.175. R = R2 - R1, Acp = 0 in the source of current with internal resistance R2.
3.176. (a) I = a; (b) CPA - tP B = 0.
3.177. PA - B = (el -
R1/(R1 + R2) = -0.5 V.
3.178. /1 = eR2/(RR1 R iR 2 R 2R) = 1.2 A, 12 = 11R1/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 1R 2/(R1 + R2).
3.181. I = (R16 2 - R261)1(RR1 R1R2+ R 2R) = 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 +
+ R3R 1 ) = 0.06 A; (b) (pA - cpB = gi 101 = 0.9 V.
3.183. I = [6 (R 2 + R3) + 0R 3]1[11 (R2 + R3) + R2R3].
3.184. TA .- (I) B = [e2R3 (R1 + R2) - g1R1 (R2 +R3)11(14112+
▪ R 2R3 R3R1) =- -1.0 V.
3.185. /1 = [R3 ((Pi - (1)2) -4- R2 (Cl
(P3)11(R1R2
R2R3
▪ R3R1) = 0.2 A.
Ri+R2
3.186. I= R2 ( R1 [I ± R2R4 (R1+ R3) /RIR 3 (11 2 R4)]
1) = 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 = 1/2e (1 e-2tniC).
3.189. (a) Q = 4/3 q 2R1 At; (b) Q = 1/2 In 2.q2R/At.
3.190. R = 3R0.
3.192. Q I (g - v) = 0.6 W, P = -IV = -2.0 W.
3.193. I = V12R; Pmax = V2/4R; 11 = 1/2.
3.194. By 2i = 2%.
3.195. T - T o = (1 - e-htic) V2/kR.
3.196. Rx =
+ R2) = 12 52.
3.197. R = R1R2I(R1 + R2);
Qyna. = (e1R2 + F 2111)214R1R2 (R1 + R2).
3.198. n
111s TrIR = 3.
3.199. Q = 1 12C6 21111(R1 + R2) = 60 mJ.
3.200. (a) AW = -1/2CV2i/(1
1) = -0.15 mJ; (b) A
= 112CV2111(1 - 11) = 0.15 mJ.
3.201. AW = -1/2 (a - 1) CV2 = -0.5 mJ,
A rnech
= 1/2 (a - 1) Cr
0.5 mJ.
3.202. h
1/2 a0 (a - 1) V2/pgd2, where p is the density of water.
3.203. (a) q = qoe-1/806P; (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.
231a//S2.
3.170. t = -RC In (I - VIVO = 0.6 tis.
3.171. p = %leo In 2 = 1.4.1013 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 -
+ R2) - e, = -4 V.
3.175. R = R2 - R1, Acp = 0 in the source of current with internal resistance R2.
3.176. (a) I = a; (b) CPA - tP B = 0.
3.177. PA - B = (el -
R1/(R1 + R2) = -0.5 V.
3.178. /1 = eR2/(RR1 R iR 2 R 2R) = 1.2 A, 12 = 11R1/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 1R 2/(R1 + R2).
3.181. I = (R16 2 - R261)1(RR1 R1R2+ R 2R) = 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 +
+ R3R 1 ) = 0.06 A; (b) (pA - cpB = gi 101 = 0.9 V.
3.183. I = [6 (R 2 + R3) + 0R 3]1[11 (R2 + R3) + R2R3].
3.184. TA .- (I) B = [e2R3 (R1 + R2) - g1R1 (R2 +R3)11(14112+
▪ R 2R3 R3R1) =- -1.0 V.
3.185. /1 = [R3 ((Pi - (1)2) -4- R2 (Cl
(P3)11(R1R2
R2R3
▪ R3R1) = 0.2 A.
Ri+R2
3.186. I= R2 ( R1 [I ± R2R4 (R1+ R3) /RIR 3 (11 2 R4)]
1) = 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 = 1/2e (1 e-2tniC).
3.189. (a) Q = 4/3 q 2R1 At; (b) Q = 1/2 In 2.q2R/At.
3.190. R = 3R0.
3.192. Q I (g - v) = 0.6 W, P = -IV = -2.0 W.
3.193. I = V12R; Pmax = V2/4R; 11 = 1/2.
3.194. By 2i = 2%.
3.195. T - T o = (1 - e-htic) V2/kR.
3.196. Rx =
+ R2) = 12 52.
3.197. R = R1R2I(R1 + R2);
Qyna. = (e1R2 + F 2111)214R1R2 (R1 + R2).
3.198. n
111s TrIR = 3.
3.199. Q = 1 12C6 21111(R1 + R2) = 60 mJ.
3.200. (a) AW = -1/2CV2i/(1
1) = -0.15 mJ; (b) A
= 112CV2111(1 - 11) = 0.15 mJ.
3.201. AW = -1/2 (a - 1) CV2 = -0.5 mJ,
A rnech
= 1/2 (a - 1) Cr
0.5 mJ.
3.202. h
1/2 a0 (a - 1) V2/pgd2, where p is the density of water.
3.203. (a) q = qoe-1/806P; (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.