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Capacitors and Dieletcrics (Charging and Discharging of Capacitance…
Capacitors and Dieletcrics
Capacitance
The capacitors is the measure of the ability of the capacitor to store energy
Capacitance of a capacitor depends on;
sizes
shapes of the conductors
the insulting placed between them
Q= CV
where
Q is the charge
C is the capacitor
V is the potential differences
Parallel Plate Capacitors
The type of capacitors which that have an arrangement of electrodes and insulating material (dielectric)
The capacitance of the parallel plate capacitors
Capacitance of concentric spheres
Capacitance = 4
π
(relative permittivity) * (permittivity of space) / (1/(inner radius) – 1/(outer radius) )
where,
C: Capacitance
ri: inner radius
ro: outer radius
k: relative permittivity
ϵ: permittivity of space
Capacitors in series and parallel
Series
Equation
Parallel
Equation
Energy stored in a charge capacitors
The energy being stored is in the form of
electric potential
Abilities;
The electronic flash in cameras and storage unit for pulsed laser
Energy storage
The energy stored on a capacitor can be calculated from the equivalent expressions:
This energy is stored in the electric field. and will have stored energy E = x10^ J
Electric field energy or energy density
The energy required can be expressed in terms of the energy per unit volume of the space between the plates having area and separation in terms of energy
Charging and Discharging of Capacitance
Charging is a process of storing energy in the capacitors
Discharging is the process of recovering the stored energy
Charging of capacitors
A battery is connected to a series resistor and capacitor, the initial current is high as the battery transports charge from one plate of the capacitor to the other
The charging current asymptotically approaches zero
The time dependent for charging of capacitors
Discharging capacitors
Energy consideration for charging and discharging of capacitors
The rate at which the battery deliver energy
The rate of energy dissipated in the resistor
The rate is stored in the capacitor
Capacitor with dielectrics
Electrical insulator is called dielectric
The functions of dielectric in a capacitor
to keep the conducting plates from coming in contact, allowing for smaller plate separations and therefore higher capacitances
to increase the effective capacitance by reducing the electric field strength, which means you get the same charge at a lower voltage
to reduce the possibility of shorting out by sparking (more formally known as dielectric breakdown) during operation at high voltage.
