Capacitor
A capacitor is a passive 2-terminal electrical component storing capacitance (electrical energy) in an electric field, made of 2 metallic plates via a dielectric plate.
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A capacitor stores electrical energy by accumulating electric charges on 2 conductive plates separated by dielectric, an insulating material. if voltage is applied, charge builds up on the plates, creating an electric field between them.
Principles
Principles
Charging
Charging
[6] This circuit has a capacitor connected across a battery and a switch controlling the current flow.
Applying voltage to a capacitor by turning on the switch creates an electric field between the 2 plates, causing negative charges to gather at a plate and positive ones to gather at the other plate.
Like magnets, charges per plate repel the same polarity charges on the opposite plate, causing both plates to have equal and opposite charges.
A dielectric subject to electric fields developping between 2 plates get polarized and reduces the electric field, and rise the plates’ capacity to hold charges. This lets each plate to store more charges, causing higher capacitance.
Note: Charges don't truly flow through capacitors as the dielectric works as an insulator, but could still flow through the power source.
Discharging
Discharging
As capacitor fully charges, the charges stay on each plates for some time before slowly leaking through the dielectric and completing the charges. But the process can speed up by connecting both plates together. As the circuit completes, positive and negative charges instantly drawn to each other prior completing the charge and release an energy burst, a process called discharging.
Components
Components
A basic capacitor has 2 ‘plates’ made of metallic conductive materials (foil, metal beads, or electrolytes) with a non-conductive part in between separating wiring leads. The non-conductive part (dielectric) stops the plates from touching which always increase capacitance (as long as it's nonconductive). Otherwise, it completes the circuit, so no charge is stored and the capacitance is infinite, and charge difference equalizes instantly.
A dielectric is a nonconductive insulation, like a glass, mica, paper, ceramics, or even air).
Often we refer to capacitor types based on material composition of the dielectric. E.g. a capacitor of a ceramic dielectric is a “ceramic capacitor.”
How dielectric increase capacitance Putting a source voltage to a circuit with a capacitor (without dielectric) separates the charge. Removing the capacitor does nothing to the charges, since the negative charges have no path to get back, and voltages, which is the same as th esource.
[3] With dielectric and without source voltage
With a dielectic between the plates, the negative charges are attracted to the positives at the other side but can't go there as the dielectric is nonconductive. But can shift to the positive plate, causing the dieelctric's atoms' charges to polarize--the atoms stretches", causing the atom's negative side to face the positive plates and positive to face the negative.
If naturally polarized materials like water is the dielectric, the attraction between the atom's negative side and the positive plate causes the atoms to rotate, causing atoms to be a bit cloesr to the plates.
All this lowers the voltage between plates and even thought, it's still the same charges on the plates, their contribution to the voltage across is partially cancelled--some contribution near both plates are negated due to having their opposite of atoms charges nearby.
As dielectric decreases voltage and charges are unaffected, using formula C = Q/V, we see that lowering voltage increases the capacitance.
E.g. If a capacitor is 4 C and 5 V: C = Q/V = 4C/5V = 800 mF is the its capacitance.
But reducing its voltage to 3 V increase the capacitance to: C = 4C/3V = 1.3 F.
With dielectric and voltage source
Adding a source voltage, it will balance the capacitor's voltage to its voltage. Since the dielectric reduces the voltage, by cancelling charges' the contribution, the battery causes more charges to separate till the capacitor's voltage equals its own voltage.
Overall, adding a capacitor with a dielectric in the capacitor increases the charge and the voltages stays the same.
Dielectric constant (k) permittivity or relative permittivity, is a measure of a material's ability to store electrical energy when subjected to an electric field
We can use a materila's dielectric material's k to know how much we've increase the capacitance.
Values and units
Values and units
[7] Capacitance (C), measured in farads (F), is how much charge a capacitor can hold, its ability to store electrons. The value is printed on a capacitor, with the rated voltage.
F is defined as the ratio of of charges, measured in coulombs (C) per plate and the voltage (V) between them: Capacitance formula: C = Q ÷ V.
E.g. A 1-farad capacitor supplied at 1 V stores 1 coulomb charges or ~6.241 × 1018 electrons.
But a very high-value unit farad, and most capacitors often used have much lower values than that, with most with these 2 prefixes:
μF as microfarads (millionths of a farad) for large capacitors
pF as picofarads (trillionths of a farad) for smaller capacitors
[6] A = an overlapping area of a capacitor's 2 plates
d = a gap between the plates
ε = a dielectric's permittivity (polarizability)
[6] Assume this model's electric field only directs between the plates and electric charge spreads evenly on them. But despite this, this model still applies to most capacitors. Aside from C = Q ÷ V, another capacitance formula is C = ϵA/d
[6] The 3 factors affecting parallel plate capacitors' capacitance:
The total overlapping area between 2 plates—bigger it is = greater capacitance.
The distance between the 2 plates—the farther they are from each other = less capacitance.
The permittivity of a dielectric material—higher permittivity of dielectric = higher capacitance.
Free air permittivity
Free air permittivity
permittivity: measure of opposition a material presents to an electric field's formation in it
[2.9] Free air permittivity/Permittivity of air/Vacuum permittivity/permittivity of free space/the electric constant (ε₀) is how air reacts to and influences an electric field. It's an ideal (baseline) physical constant. Its CODATA value is ε0 = 8.8541878188(14)×10−12 F⋅m−1.
Permeability
Permeability
Analogies
Analogies
[6] Compare a capacitor's function to a spring: If left alone, a spring stays in the resting position or equilibrium, like a capacitor. As energy exerts on it by pushing it down, it stores the energy as potential energy. Akin, electrical energy in a capacitor stores electric charges as potential energy.
Symbols
Symbols
[1]
Types
Types
[1], [2.7] Various capacitors are classified as fixed and variable.
Fixed capacitors have a constant capacitance value, can be further classified into polarized and non-polarized, including ceramic, electrolytic, film, and others. Variable capacitors, like trimmers and tuning capacitors, allow for adjusting capacitance.
Ceramic capacitors are used in audio to RF, with a value of a few picofarads to ~0.1 microfarads, widely used both in leaded and surface mount formats.
Electrolytic capacitors are polarized capacitors, with high capacitance values (often above 1uf), for low frequency applications (power supplies, decoupling and audio coupling applications)
Tantalum capacitors are also polarized and give a very high capacitance for their volume, consisting of a tantalum metal pellet as anode. It's intolerant to be reversed biased. Reverse voltage can destroy it.
Silver mica capacitors are high level stability, low loss accuracy
Parallel plate capacitors are
Fixed Capacitors
Fixed Capacitors
[6]
a capacitor
a ceramic capacitor
Mica capacitors
E.g. A mica capacitor has a plate area of 0.2 m2. The thickness of the dielectric is 3 mm. What is the capacitance? Express your answer in nF to 2 decimal places. Only include the numerical value (no units) in the answer space.
E.g. 1# A mica capacitor has a plate area of 0.2 m² at 3 mm dielectric thickness.
What's the capacitance?
ϵr = κ = ~5.4
ϵ0 = 8.854x10⁻¹²
A = 0.2 m²
d = 3 mm = 0.003 m
C = ϵ0*ϵr*(A/d) = (5.4*8.854*10⁻¹²*0.2)/0.003 = 3.19 nF is the capacitance.
E.g. 2# A 58 µF, 338 µF and 91 µF capacitor are in series.
Find the CT.
CT in series = 1/C1⁻¹ + C2⁻¹ + C3⁻¹): 1/(58⁻¹ + 338⁻¹ + 91⁻¹) = 32.06 µF =32.06x10⁻⁶ = 0.00003206 F is the total capacitance.
3# A 0.2 µF, 0.5 µF and 0.9 µF capacitor are in series, via a 15 V battery connected.
Find the 0.5 µF capacitor's voltage?
CT = 1/(0.2⁻¹ + 0.5⁻¹ + 0.9⁻¹) = 0.123287671 µF
Note: Voltage (V) doesn't need conversion when working with microfarads (µF) and microcoulombs (µC).
Q = VC = 15 x 0.123 = 1.85 µF
V = Q÷C = 1.85/0.5 = 3.7 µC
Capacitor relative permittivity
Capacitor relative permittivity
[2.8]
Filtered capacitor
Filtered capacitor
A filtered capacitor smooths or filters a circuit's voltage/current (e.g., reduce ripple in power supplies or noise in signals), acting as a low-pass filter (shunts AC to ground while passing DC).
It stores charge during voltage peaks and releases it during dips, stabilizing output.
Many capacitors types are used as filters:
Electrolytic (aluminum/tantalum):
Why? High capacitance (µF to mF) for low-frequency ripple (e.g., power supply filters).
Example: Smoothing output in a bridge rectifier (like your lab circuit).
Ceramic (MLCC):
Why? Low ESR, fast response for high-frequency noise (e.g., decoupling in digital circuits).
Film (Polypropylene/Polyester):
Why? Stable, low-loss for precision filtering (e.g., audio or motor drives).
Ripple voltage formula: Vripple = (Vpkload x t)/R*C = (I*T)/C
Average voltage: Vavg = DC = Vpkload - (Vripple/2)
[1.4] Rectifier circuits A filter capacitor is crucial in rectifier circuits (half-wave, full-wave, and bridge) by converting pulsating DC to smoother DC.
Half wave:
With a filter capacitor, a capacitor charges to Vpk during connections and discharges through loads during gaps.
Ripple voltage formula: Vripple ≈ Iload/fC
Average DC voltage (Vavg) formula: Vavg = Vpk - (Vripple/2)
Without a capacitor, output is pulsating DC via gaps, only conducting during positive half cycles.
Average DC voltage (Vavg) (no load) formula: Vavg = Vpk/π
Full wave:
With a filter capacitor, ripple is halved compared to half-wave (due to 2f)
formula: Vripple = Iload/2fC
Without a capacitor, output is pulsating DC via gaps, only conducting during positive half cycles.
Average DC voltage (Vavg) (no load) formula: Vavg = 2*Vpk/π
Bridge circuit:
With a filter capacitor, ripple formula same as full-wave (Vripple = Iload/2fC).
Without a capacitor. it's akin to full-wave (conducts on both half-cycles), but via 2 diode drops (Vpk = Vsec - 1.4V)
Average DC voltage (Vavg) (no load) formula: Vavg = 2*Vpk/π
Summary
Capacitor charge
Capacitor charge
[1.2] A charge in a capacitor is a voltage amount given
Closing this circuit's switch causes a high voltage rise, going from 0 V to the supply voltage (BAT1) in 5τ (time constant).
A time constant (τ "tau") depicts how fast a system changes.
The time constant of this capacitor is the resistance times capacitance (of the circuit): ΤC = R1xC1--the resistance is from R1 through C1, back to the source.
Capacitor voltage formula: VC = V0*(1-e)^(-τ/t)
VC = capacitor charging voltage
V0 = source voltage
V naught/nought or V-zero ("V0") represents an object's velocity at a given time period.
[2.6] nought/naught: British use of number zero
e = Euler's number (~2.718)
τ = RC = time constant (Tau)
t = time (in seconds)
Note: Time ("t") is often 1-5τ
The capacitor charging voltage formula:
The capacitor's voltage will charge til it reaches its max capacity (the full charge), as shown by this graph.
Capacitor discharge
Capacitor discharge
[1.2] A discharge in a capacitor is when it releases the energy it stored and send scurrent across a circuit, occuring if a circuit's voltage is under a capacitor's stored voltage.
Fig 1.
Opening this switch causes a discharge right away.
Fig. 2, The discharge causes a fast voltage decent, to almost 0 V.
If the switch is closed for +5τ, the Vτ = source voltage.
If the switch opens at 3τ, the capacitor (C1) voltage is lower.
If the switch opens for 10s, the current goes in the opposite way, only in the 2nd loop, but not into the first loop due to the opened switch (Fig 1).
So, now C1 is a temporary DC source, going into R1 and R2.
If C1 does reaches its max voltage, the voltage source starts at the same amount.
Regardless the current cannot currently reach loop 1, C1 and R2's polarity is the same as if the circuit's was charging. Only R1's polarity is reversed compared to the circuit's charging state, giving it a negative current, therefore a negative voltage (Fig 2).
The capacitor discharging voltage formula: VC = V0e^(-τ/t)
VC = capacitor discharging voltage
V0 = initial capacitor voltage
e = Euler's number (~2.718)
τ = RC = time constant (Tau)
t = time (in seconds)
Note: Time ("t") is often 1-5τ
For the discharge's tau, the current in the second loop links to the C3. Since R2 is now part of the second loop, the discharge's tau: ΤC = (R1 + R2)xC1.
Overall If V0 in Fig. 2 reaches the full charge, it equals the voltage supply (BATS in the circuit).
If V0 doesn't reach full charge, it maybe like 50-60-70% of the supply.
References
References
[1] Why and How to use capacitor | Basic electronics Tutorials - YT
[2.1] Capacitor
[2.2] RC circuit
[2.3] Exponential decay
[2.4] Time constant
[2.5] Silver mica capacitor
[2.6] Names for the number 0 in English#"Nought"_and_"naught"_versus_"ought"_and_"aught"
[2.7] Capacitor types
[2.8] Relative permittivity
[2.9] Vacuum permittivity
[3] NCERT Physics Grade 12 Unit 2: Dielectric in Capacitors - Khan Academy
[4] Introduction to Capacitors, Capacitance and Charge - Basic Electronics Tutorials
[5] Capacitance and its Calculation, Dielectric, Dipoles and Dielectric Absorption - DOEEET
[6] ElecCircuit
[7]
Quizzes
Quizzes
[Q1] Flashcards
[Q2] Exercises
[Q3] Homework-capacitance - Canva
[Q3.1] ELE8922: Jan 13-sec 010
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