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General Values and Vectors by S.S. Education, Kota |
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CAPACITANCE
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Parallel-Plate Capacitor:
C = k Î0 (A/d)
C = capacitance [farads F]
k = the dielectric constant (1)
e0 = permittivity of free space
8.85 × 10-12 C2/N·m2
A = area of one plate [m2]
d = separation between plates [m]
Cylindrical Capacitor:
C = capacitance [farads F]
k = dielectric constant (1)
Î0 = 8.85 × 10-12 C2/N·m2
L = length [m]
b = radius of the outer
conductor [m]
a = radius of the inner
conductor [m]
Spherical Capacitor:
C = capacitance [farads F]
k = dielectric constant (1)
Î0 = 8.85 × 10-12 C2/N·m2
b = radius, outer conductor [m]
a = radius, inner conductor [m]
Maximum Charge on a Capacitor: [Coulombs C]
Q =VC Q = Coulombs [C]
V = volts [V]
C = capacitance in farads [F]
For capacitors connected in series, the charge Q is equal for
each capacitor as well as for the total equivalent. If the
dielectric constant k is changed, the capacitance is
multiplied by k, the voltage is divided by k, and Q is
unchanged. In a vacuum k = 1, When dielectrics are
used, replace Î0 with k Î0.
Electrical Energy Stored in a Capacitor: [Joules J]
U = Potential Energy [J]
Q = Coulombs [C]
V = volts [V]
C = capacitance in farads [F]
Charge per unit Area: [C/m2]
s =q/A
s = charge per unit area [C/m2]
q = charge [C]
A = area [m2]
Energy Density: (in a vacuum) [J/m3]
u = 1/2 Î0 E2
2 u = energy per unit volume [J/m3]
Î0 = permittivity of free space
8.85 × 10-12 C2/N·m2
E = energy [J]
Capacitors in Series:
Capacitors in Parallel:
Ceff = C1 + C2 …….
Capacitors connected in series all have the same charge q.
For parallel capacitors the total q is equal to the sum of the
charge on each capacitor.
Time Constant: [seconds]
t = RC
t = time it takes the capacitor to reach 63.2% of its maximum charge [seconds]
R = series resistance [ohms ohm]
C = capacitance [farads F]
Charge or Voltage after t Seconds: [coulombs C] charging:
q= Q( 1-e-t/t )
V = Vs (1- e-t/t )
discharging:
q = Qe-t /t
V =Vs e-t/t
q = charge after t seconds
[coulombs C]
Q = maximum charge [coulombs
C] Q = CV
e = natural log
t = time [seconds]
t = time constant RC [seconds]
V = volts [V]
Vs = supply volts [V]
[Natural Log: when eb = x, ln x = b ]
Drift Speed:
&#Q = # of carriers × charge/carrier
&#t = time in seconds
n = # of carriers
q = charge on each carrier
vd = drift speed in meters/second
A = cross-sectional area in meters2
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