EE115. Chapter 16

16.2

C =Q/U,    Q = C*U
a) $5*10^{-7}$ C

b) $2*10^{-6}$ C

c) $1.5*10^{-5}$ C

d) $2.5*10^{-5}$ C

e) $5*10^{-5}$ C

16.4

$C =Q/U$,   $U = Q/C$
a) 250 V

b) 150 V

c) 10 V

d) 1000 V

e) 40 V

d) 5 V

16.6.

$C = \epsilon*S/d$

where $\epsilon$ is the electrical permittivity of the material between plates, S is the area of the plates and d is the distance between plates.

Physical factors are

1. type of dielectric material.

2. distance between plates.

3. plates surface area

16.8

a) 472M  it means $47*100 = 4700 pF = 4.7 nF$ with tolerance +,- 20%

b) 103J it means $10*1000 =10000 pF = 10 nF$ with tolerance +,- 5%

c) 224K it means $22*10000 pF=220 nF$ with tolerance +,- 10%

d) 273J it means $27*1000 =27000 pF =27 nF$ with tolerance +,- 5%

e) 101J means $10*10 =100 pF$ with tolerance +,- 5%

f) 569F  means $56*10^9 pF = 56*10^9*10^{-12} F =56*10^{-3} F = 56 mF$ with tolerance +,- 1%

g) 104K means $10*10000 pF = 100 nF$ with tolerance +,- 10%

h) 332M means $33*100 pF = 3.3 nF$ with tolerance +,- 20%

i) 680J means 68 pF with tolerance +,- 5%

16-10.

a) red, $violet * 10^{black}$, tolerance gold

$27*10^0 =27 pF$ tolerance 5%

b)$10*10^2 =1000 pF =1 nF$ tolerance 10%

c) $47*10^1 =470 pF$ tolerance 10%

16.12

a) 56 means 56 pF

b) C3 means 0.3 pF

c) U4 means 0.1 microF

d) 22 means 22 pF

16.14

a) yellow, $violet *10^{yellow}$, tolerance silver

$47*10^4 pF = 470 nF$ tolerance 10%

b) $62*10^5 pF = 6200 nF =6.2 microF$ tolerance 5%

c) $15*10^6 pF =15 microF$ tolerance 10%

d) $82*10^7 pF = 820 microF$ tolerance 5%

16.16

Z5U means Z=+10 degree Celsius low temperature limit, 5=+85 degree Celsius high temperature limit, U=+22%/-56% variation of the capacitance from the 25 degree Celsius value

16.18

$C_{equivalent} = C1+C2+C3 =0.1 +0.27 +0.01 =0,38 microF$

16.20

a) $V1=V2=V3 = 10 V$

b) $C = Q/U$,   $Q1 = C1*U1 =100*10^{-6}*10  =100*10^{-5} C = 10^{-3} C$
c) $Q2 = C2*U2 =220*10^{-6}*10 =2.2 *10^{-3} C$

d) $Q3 =C3*U3 =680*10^-6*10 =6.8 *10^{-3} C$

f)  $C_{equivalent} = C1+C2+C3 =100 +220+680 = 1000 microF =1 mF$

e) $Qtot = Ceq*U = 10^{-3}*10 =10^{-2} C$

16.22

C1 = 1500 pF    C2 =1 nF =1000 pF
Cseries = C1*C2/(C1+C2) = 600 pF

16.24

a) $1/Ceq = 1/c1+ 1/c2 +1/c3 = 10^6/10 +10^6/30 +10^6/15$

$Ceq = 5*10^-6 F = 5 microF$

b) $Q = I*t = 180 microA*1s =180 microC =180*10^{-6} C$

c) $C= Q/U$,    $U= Q/C$
$U1 =180*10^{-6}/10*10^{-6} =18 V$

$U2 =180/30 = 6V$

$U3 =180/15 = 12 V$

d) $Q = Ceq*U = 5*10^{-6}*35 =175*10^{-6} C =175 microC$

16.25

1/Ceq = 1/C1+1/C2

1/C2 =1/Ceq-1/C1

C2 =C1*C2/(C1-C2) = 120*100/(120-100) = 600 pF

16.28

a) $W =C*U^2/2 = 27*10^{-9} *20/2 =2.7*10^{-7} J$

b) $W =135*10^{-6} J$

c) $W =675*10^{-6} J$

16.30

a) 0.047 microF = 47 nF = 47000 pF

b) 0.0015 microF =1.5 nF = 1500 pF

c) 390000 pF = 390 nF = 0.39 microF

d) 1000 pF = 1 nF = 0.001 microF

16.32

154K means 15*10000 pF = 150 nF tolerance 10% = 15 nF

it means maximum value 165 nF, minimum value 135 nF

0.160 microF =160 nF is within tolerance

16.34

229B means 2.29 pF tolerance 0.10%= 0.0023 pF

it means maximum value 2.292 pF, minumum value 2.287 pF

2.05 pF is not within tolerance

16.36

The capacitor will charge from the current provided by the ohmmeter. The ohmmeter will indicate an increasing voltage on the capacitor until a saturation value which represent the maximum charging voltage of the capacitor.

the time constant of capacitor charging is tau = R*C =10K *0.47 microF =4.7*10^-3 sec

it means after time=tau the capacitor will reach a voltage equal to (Vmax/e)

16.38

N500 means a variation of the capacitance of -500 ppm/degree Celsius from 25 standard value temperature

a) 75 -25 =50 degree Celsius variation $= -500*10^{-6}*50 *100pF =-2.5 pF$ variation

C =100-2.5 =97.5 pF

b) 125 -25 =100 degree Celsius variation $= -500*10^{-6}*100*100pf  = -5 pF$

C = 100 – 5 =95 pF

c) -25 -25 =-50 degree Celsius variation $= -(-500)*10^{-6}*50*100pF = +2.5 pF$

C =100+2.5 =102.5 pF