A device to store charge or electrostatic energy is called a capacitor.
Capacitance it is the capacity of a capacitor to store charge. In a capacitor Q ∝ V or Q = CV; C is called the capacitance
C = (M1 L-2 T4 A2)
According to shapes, capacitors may be of three types: spherical parallel plate and cylindrical.
Unit of capacitance is faraday 1F (IC/IV)
IF is a very big unit, Therefore, µF or nF or µµ F (pF) and so on are used.
Spherical capacitors may be of two types
Isolated spherical capacitor
Concentric spherical capacitor
Isolated spherical capacitor is a single sphere. Its capacitance is given by C = 4πε0R where R is radius of the sphere.
Two concentric spherical shells or the inner one may be solid.
C = 4πε0 (R2 R1) / (R2 - R1)
If a dielectric of strength K is introduced between R1 and R2
C = 4πε0 k R2 R1 / R2 - R1
Parallel plate capacitor
If A is area of each plate and d is the separation between two plates then
C = ε0 (A/d) with free space as dielectric
C = Kε0 (A/d) if a dielectric of strength k is added
If the dielectric slab has thickness t (t < d) then
If a dielectric of strength k is introduced in between electrolytic capacitors may have high values and go upto mF.
Capacitance of a cylindrical capacitor
C = 2πε0l / log e r2 / r1
If the space between two cylinders is filled with a dielectric of strength k then
C = 2πε0kl/r2
Log e r1
Magnitude of induced charge Qp = Q [1 - /1 / k]
Force between the plates of a capacitor (attractive force)
F = (Q2/2) A ε0
Energy stored (electrostatic) in a capacitor
U = (1/2) CV2 = Q2/2C = QV/2
Energy stored per unit volume = [(1/2) ε0E2]
Where E is electric field intensity. The capacitance of a variable tuning capacitor (used for tuning radio) having n plates is
C = (n - 1)A ε0/d where d is the separation between each plate.
If dielectrics are added in the manner shown, then the net capacitance from equivalent circuit is a parallel combination of C1, C2 and C3 Hence
C1 = ε0 K1 [(A/3)/d] C2 = ε0 K2 [(A/3)/d] C3 = ε0 K3 [(A/3)/d]
If the dielectrics are arranged as shown in ten from equivalent circuit it is evident that the net capacitance is a series combination of C1, C2 and C3
ExpertsMind.com - Capacitors Assignment Help, Capacitors Homework Help, Capacitors Assignment Tutors, Capacitors Solutions, Capacitors Answers, Electromagnetism Assignment Tutors