Capacitance Hw

 

M1.          D

[1]

M2.          B

[1]

M3.          D

[1]

M4.          C

[1]

Time Constant = -10/ln(0.5)

           Time Constant = 14s

M5.          D

[1]

M6.          B

[1]

 

M7.          A

[1]

 

8.       (a)     (i)      Cp = 2 + 4 = 6 μF                                                                                   A1

  (ii)   1/C = 1/2 + ¼                                                                                         C1
Cs = 4/3 =1.33 μF                                                                                  A1

  (b)   (i)      6.0 V                                                                                                     A1

  (ii)   Q = CpV                                                                                                C1
= 6 × 6 = 36 μC                                                                                     A1

  (c)    E = ½ CsV2                                                                                                     C1
= 2.4 × 10–5                                                                                                    A1

  (d)   (i)      The capacitors discharge through the voltmeter as it has a high resistance  B1

  (ii)   V = V0e–t/CR
(1/4) =e–t/(6×12)                                                                                       C1
ln (¼) = t / 72                                                                                         C1
t = 72 ln 4 ≈ 100 s                                                                                  A1

[12]

  9.     (a)     (i)      Q = VC; W = ½ VC.V ( = ½ CV2) (2)

(ii)     parabolic shape passing through origin (1)
plotted accurately as W = 1.1 V2 (1)                                                           4

  (b)   (i)      T = RC; = 6.8 × 103 × 2.2 = 1.5 × 104 s = 4.16 h                                         2

(ii)     ΔW = ½ C(V12 –V22) = 1.1(25 – 16) ; = 9.9 (J)                                           2

  (iii)  4 = 5 exp(–t/1.5 × 104) ; giving t = 1.5 × 104 × ln 1.25 = 3.3 × 103 (s)          2

(iv)    P = ΔW/Δt = 9.9/3.3 × 103 = 3.0 mW                ecf b(ii) and (iii)                 1
allow P = Vav2 /R = 4.52/6.8 × 103 = 2.98 mW

[11]