rs are connected in the series/parallel arrangement shown in the sketch /Six cap

Question

rs are connected in the series/parallel arrangement shown in the sketch /Six capacitors The equivalent capacitance between points a and b is: , b 3C A) 4C/7 B) C/3 C) 3C/5 D) 2C/3 E) 2C/5 3C 8. A 6.0-pF capacitor charged to 50 V and a 4.0-uF capacitor charged to 34 V are connected to each other, with the two positive plates connected and the two negative plates connected. What is the total energy stored in the 6.0-pF capacitor at equilibrium? A) 6.1 mJ B) 7.0 mJ C) 0.8 mJ Q.CU 5.7 mJ E) 6.6 mJ 9. A nichrome wire and an aluminum wire, cach with the same initial resistance have the same change in resistance when heated separately. (pAi-2.82 x 10" -m; -39 x 10" / °C; Anchrome-1.50 x 10-0 -m; Ghichrome 0.40 x 10 /°C.) The ratio of the temperature change of the nichrome wire to the temperature change of the aluminum wire is A) 0.019, B) 9.8. C) 53. D) 0.10. E) 0.18 AT-Uni-.-2499.99 .in 26 Page 3 of 9

Explanation / Answer

7)(c)3C/5

explanation:

We see from the circuit that

two C and connected in series so theie equivalent is

C' = C x C/(C + C) = C/2

Now these two C/2 are in parallel so they sums to

C'' = C/2 + C/2 = C

Now 3C ; C and 3C are in series so

1/Ceq = 1/3C + 1/C + 1/3C = 1/C (1/3 + 1 + 1/3) = 5/3C

Ceq = 3C/5

Hence(c) 3C/5

8)(d)5.7 mJ

explanation:

We know that charge is conserved

Q1 + Q2 = 6 x 50 + 4 x 34 = 436 uC

V1 = V2

Q1/C1 = Q2/C2

Q1/6 = Q2/4

Q1 = 3/2 Q2

Q1 + 3/2 Q2 = 436 uC => Q2 = 174.4 uC

Q1 = 261.6

U = 1/2 Q^2/C = 0.5 x 261^2 x 10^-12/6 x 10^-6 = 5.7 x 10^-3 J = 5.7 mJ

Hence, (d)5.7 mJ

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