Fundamentals of Capacitors
Fundamentals of Capacitors
Introduction
A capacitor is a two-terminal electronic device that stores electric charges, and it is a passive component. It requires a minimum of two conductive plates or mediums separated by a non-conducting material or medium. The universally used non-conducting materials in the capacitor are Oxide layer, papers, thin plastic film, ceramic, glass, mica, or air medium. It can store limited electric energy in a fast manner when compare to chargeable batteries but in a different form.
Capacitor operation
Water tank analogy
Let (i) a water tank has one inlet and one outlet, outlet valve closed, and the inlet valve opened to fill the tank with water. (ii) The inlet valve has closed, and the outlet valve opened to reduce water in the tank. The water tank filling or emptying rate depends on the capacity of the tank and water inlet and outlet flow rate. Similarly, the charging time of the capacitor depends on the capacitor value and the flow of charges. Capacitor value entirely depends on the area of plate and property of dielectric material used. Each dielectric material has a specific dielectric constant. A fixed or variable voltage source can charge the capacitor, and the amount charge stored across the capacitor plates will indicate its capacity.
q = C x V ———– (1)
Where
C = Capacitance
q = Charge stored across the plates
V = Applied electric potential
Charge across the capacitor
Initially, the charge stored in the capacitor plate is zero, and the voltage across its plates also zero. The capacitor will offer a minimum resistance for charge flow immediately after connecting a battery (transient period). The charge flow will gradually decrease and become zero because the dielectric material present between the conductive plates will not allow the change to move from one side to another side.
Due to this, the electrons will accumulate in one of the capacitor plates depending on battery polarity. After giving the DC supply or battery voltage to the capacitor circuit, it will behave like an open circuit under a steady-state condition. Now, the voltage across the plates will be equal to the battery potential, and this voltage developed due to the gradual accumulation of charged particles across the plates.
The accumulated charge will spread across the plates and develop a charge density σ = q/A where A = area of the capacitor plate. The charges stored across the plates will discharge slowly and become zero when connecting the capacitor to a load after disconnecting from the battery.
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Basic capacitor equation
Electric field strength (E) between two capacitor plates= Force / Unit charge or
E = σ/ε = σ/εrεo ——— (2)
Where εr = Relative permittivity of dielectric material available in between the two capacitor plates, εo = 8.854 x 10-12 Farad per meter = Permittivity of space, εr = 1 for air or free space
The voltage across the capacitor plates V = Integral [E] with limits 0 to d and V =Ed where d= distance between two plates
From equation (1) and (2)
V = Ed = q/C = σd/ε
qε =Cσd where charge density σ = q/A
qε =qCd/A
C=εA/d = εrεoA/d
The value of the capacitor is directly proportional to the area of the capacitor plate & the relative permittivity of the dielectric material and inversely proportional to the distance between two plates.
Energy stored in capacitor
Electric field strength (E) = Force / Unit charge =F/q in Newton/Coulomb
Multiply capacitor plate separation distance (d) by both sides of the equation.
Electric field strength x distance = E x d = (F x d)/q =W/q
Where, Work done (W) = Force x Distance = F x d in Newton-Meter
The product of electric field strength and distance = Voltage across the plates = Potential difference between the plate.
E x d = ∆V = V =W/q and W= V x q. ———— (3)
Let the battery will deliver a fractional change in charge under the constant potential.
From equation (3)
dW = V x dq ——– (4)
From equations (1) and (4)
dW = (q/C) x dq ——– (5)
The average value of work done during charging of the capacitor from 0 to a charge q can be calculated by integrating the equation (4)
Integral [dW] = W = Integral [(q/C) x dq] with limits 0 to q,
W = [q2/(2C)] ——- (6).
From equation (1) and (6),
Work or measure of energy stored across capacitor = U=CV2/2.
The response of the capacitor for AC and DC inputs
The response of the capacitor DC inputs:
Current is the rate of change of charge, and from equation (1).
Current I = dq/dt= C x dV/dt ——- (7).
The result for differentiating a constant is zero.
From equation (7), Applying a constant voltage, battery, or Direct Current (DC) input to the capacitor, the current through the capacitor is zero, and it is an open circuit for constant input voltage. A load may be connected or terminals short-circuited to discharge the accumulated charges from the capacitor.
Integrating the equation (7) and rearranging, the voltage across the capacitor is given by,
V=1/sC x I —— (8).
The capacitor impedance = V/I = 1/sC. ——– (9)
Where the letter s is a complex number, and it is expressed as s = α + jω.
The response of the capacitor AC inputs
The commonly known Alternating Current (AC) is a sinusoidal signal. The sinusoidal signal does not have a stable part, and its real part or α is zero.
From equation (9)
The capacitor impedance = 1/(jωC) ——– (10)
The phase angle is tan-1(0) -tan-1(imaginary part/Real part) = -tan-1(Infinite) = -90o. The capacitors are having a leading power factor because and the current will lead the voltage by 90o. i.e., the voltage developed across the capacitor is due to the accumulation of charges across the capacitor plates.
Where ω is in radian and ω = 2πf and substituting ω in equation (10)
The capacitor impedance = 1/(j2πfC) ——– (11)
From equation (11), Applying an AC input to the capacitor, the charge flow starts between the capacitor plates. During the positive half cycle of the sinusoidal signal, electrons will accumulate one side of the capacitor plate, and the negative half cycle will mobilize stored electrons from one plate to another and vice versa. The applied frequency is maximum or very high value, the capacitor impedance will become approximately zero, and current or charge flow between the plates are maximum. The capacitor behaves like a short circuit for high or very high-frequency AC signals.
Polarized and nonpolarized capacitor
The polarized and nonpolarized capacitors work similarly. The nonpolarized or bipolar capacitor does not have specific polarity. The capacitor terminal or electrodes are polarity free, and they have the privilege to connect with either positive or negative parts of a circuit. A capacitor will have two conductive plates and a dielectric material like ceramic, thin plastic film, paper, or mica. It gives stable capacitance, less leakage current for high-temperature variations, satisfactory frequency response, and better accuracy. The only problem with this is the physical size of the capacitor increases with an increase in capacitance value.
The polarized capacitor has two conductive plates, and they are coated with an oxide layer. An electrolytic dielectric material (A thin dielectric material saturated with electrolyte liquid) is embedded between the plates. The electrolyte coated on the thin dielectric will occupy a large surface area and act as a cathode.
Properties of polarized capacitors
- It can give a larger capacitance in a compact structure.
- It can store a large amount of charge and a shorter lifespan.
- The charge stored across the plates will vary due to temperature change.
- The capacitor is polarity sensitive.
- It has less stability and offers more leakage current.
Conclusion
The capacitors are used in DC blocking, signal filtering, motor starting, touch screens, keypads, microphones, coupling, and decoupling applications. The charge stored across the capacitor is discharged to trigger a control circuit, and capacitors are used to design dynamic random-access memory.
The capacitors are also used as sensors. The change in the physical quantity is allowed to change the dielectric strength, area of the capacitor plate, or distance between the plates of the capacitors, the phenomenon will increase or decrease the capacitor value, and it is used to detect a physical quantity in terms of change in capacitance. The capacitor can hold the charge for a particular period even after removing it from the circuitry, and it will depend on the quality of the capacitor. It is not safe to touch the capacitor terminals in freehand.
