quantity symbol unit unit abbreviation -------------------------------------------------------------------------- angular frequency ω radian/second rad/s capacitance C farad F charge Q, q coulomb C current I, i ampere A electric field strength E (fancy) volts/meter V/m newtons/coulomb N/C energy, work W, w joule J magnetic flux density B tesla T frequency f hertz Hz impedance Z ohm Ω inductance L henry H magnetic flux Φ weber Wb mmf F (fancy) amp-turns At period T seconds s power P, p watt W reactance X ohm Ω reluctance R (fancy) amp-turns/weber resistance R ohm Ω time t second s voltage V, v, E, e volt V
The total resistance of 2 resistors in parallel is the product of their resistance divided by their sum.
RT = (R1 * R2) / (R1 + R2)
The total resistance of multiple resistors in parallel is:
RT = 1 / ((1 / R1) + (1 / R2) + ... + (1 / RN))
Voltage division:
Vout = Vin * (R2 / (R1 + R2)) ;Where R1 is connected to positive
The total capacitance of capacitors in parallel is the sum of the capacitors.
CT = C1 + C2 + ... + CN
The total capacitance of 2 capacitors in series is the product of their capacitance divided by their sum.
CT = (C1 * C2) / (C1 + C2)
The total capacitance of multiple capacitors in series is:
CT = 1 / ((1 / C1) + (1 / C2) + ... + (1 / CN))
The insulator between the conducting plates is called the dielectric.
The amount of charge (Q) that a capacitor can store depends on the applied voltage.
Q is proportional to voltage.
Q = CV or C = Q / V
Capacitance is proportional to plate area.
Capacitance is inversely proportional to plate spacing.
Capacitance depends on the dielectric.
C = E(symbol) * A / d
Where:
A is the area of plates in meters squared;
d is the plate spacing in meters;
E is the absolute dielectric constant of the insulating material in farads per meter (F/m).
The absolute dielectric constant of air or a vacuum, Eo = 8.85 * 10-12 F/m.
E = Eo * Er
eg. oil = 35.4 * 10-12
Dielectric breakdown, is when the capacitors voltage is high enough, that the force on the electrons is so great, they are literally torn from their orbit.
The dielectric strength is the electric field intensity at dielectric breakdown.
Solid dielectrics are damaged by breakdown.
Relative dielectric constants (relative permittivities) E(symbol)r -------------------------------------------------------------------- Vacuum 1 Air 1.0006 Ceramic 30 to 7500 Mica 5.5 Mylar 3 Oil 4 Paper (dry) 2.2 Polystyrene 2.6 Teflon 2.1 Dielectric strength (kV/mm) --------------------------- (These values depend on the composition of the material) Air 3 Ceramic (high Er) 3 Mica 40 Mylar 16 Oil 15 Polystyrene 24 Rubber 18 Teflon 60 Conversion Factors ------------------ 1 tesla = 104 gauss 1 weber = 108 lines Constants --------- Permeability of free space µo = 4 *pi * 10-7 Wb/A-m Permittivity of free space (E)o = 8.854 * 10-12 F/m Charge on an electron Qe = 1.602 *10-19 C
-b ± sqrt(b2 - 4ac)
x1,2 = ---------------------
2a
if (b2 - 4ac) >= 0, then the roots are real
if (b2 - 4ac) < 0, then the roots are complex conjugates