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Capacitors (1 of 9) What is a Capacitor, An Explanation Capacitance of a Capacitor, Where, -> Capaci...

Capacitors (1 of 9) What is a Capacitor, An Explanation

Capacitance of a Capacitor,

$C=k\times{\varepsilon\underset{0}{}\frac{A}{d}$

Where,

$C$ -> Capacitance, in Farad
$k$ -> Di-electric Constant, a Number
$\varepsilon\underset{0}{}$ -> Permittivity of Free Space, $({8.85}\times{10^-12}\times\frac{F}{m})$ (or) $({8.85}\times{10^-12}\times\frac{C^2}{Nm^2})$
A -> Area, in Square Meter
d -> Distance between Plates, in Meter
N -> Newton
m -> Distance, in Meter

$Capacitance(Farad,F)=\frac{Charge(Coulomb,C)}{Voltage,(Volt,V)}$
$F=\frac{C}{V}=\frac{C^2}{Nm}$

Capacitors (2 of 9) What is Capacitance? An Explanation

Capacitance of a Capacitor,

$Q={C}\times{V}$

Where,

$Q$ -> Charge, in Coulomb
$V$ -> Potential-Difference/Voltage, in Volt
C -> Capacitance, in Farad

Capacitors (3 of 9) What is a Farad? An Explanation

Unit of Capacitance, Farad,

$C=\frac{Q}{V}$

Where,

$Q$ -> Charge, in Coulomb
$V$ -> Potential-Difference/Voltage, in Volt
C -> Capacitance, in Farad

Capacitors (4 of 9) Calculating the Capacitance of a Capacitor, An Explanation

Calculating Capacitance of a Capacitor, Examples,

Example 4.1) Calculate Capacitance in a parallel plate capacitor, having plates of Area 0.525 $m^2$ , separated 2.5mm apart with Air as dielectric medium.

$C=k\times({\varepsilon\underset{0}{})\times\frac{A}{d}$

$C=1\times{8.85\times{10^-12}\times\frac{C^2}{Nm}}\times\frac{0.525^2}{2.5\times{10^-3}}=2.16\times{10^-9}F$

where,

$\frac{C^2}{Nm}=F$

Example 4.2) Calculate Capacitance in a parallel plate capacitor, having plates of Area 5cm x 10cm $m^2$ , separated 2cm apart with Bakelite as dielectric medium (k=4.7).

$C=4.7\times{8.85\times{10^-12}\times\frac{C^2}{Nm}\times\frac{5\times{10^-3}}{2\times{10^-2}}=1.04\times{10^-11}F$

Capacitors (5 of 9) Calculating the Capacitance of a Capacitor, Worked Examples

Calculating Capacitance of a Capacitor, Examples,

Example 5.1) Calculate Capacitance in a parallel plate capacitor, having plates of dimensions 20cm x 3cm, separated by a 1mm Air gap.

$C=1\times{8.85\times{10^-12}\times\frac{C^2}{Nm}}\times\frac{2x3x10^-3}{1\times{10^-3}}=5.31\times{10^-11}F$

Example 5.2) Calculate Capacitance in a parallel plate capacitor, having circular plates of Radius 5cm, separated by a piece of plastic of 25um thick, having dielectric medium (k=2.2).

$C=2.2\times{8.85\times{10^-12}\times\frac{C^2}{Nm}\times\frac{\pi{5^2}\times{10^-4}}{25\times{10^-6}}=6.11\times{10^-9}F$

Capacitors (6 of 9) Factors Affecting the Capacitance of a Capacitor

Factors affecting Capacitance of a Capacitor,

where,

A -> Area, in Square Meter
d -> Distance between Plates, in Meter
k -> Dielectric Constant of material between the plates

Capacitors (7 of 9) Energy Stored in a Capacitor, An Explanation

Energy Stored in a Capacitor,

$W=q\Delta{V}$
$W=\frac{1}{2}QV$

   $Q=CV$
   $W=\frac{1}{2}CV^2$
   $V=QC$
   $W=\frac{1Q^2}{2C}$

where,

W -> Energy to get Work done, in Watt
q -> Electron Charge, in Coulomb
Q -> Total Capacitor Charge, in Coulomb
C -> Capacitance, in Farad
V -> Potential Difference/Voltage, in Volt
$\Delta{V}$ -> Difference in Potential Energy to move a charge, in Volt

Capacitors (8 of 9) Energy Stored in a Capacitor, Example Problems

Calculating Capacitance of a Capacitor, Examples,

Example 8.1) How much work does a 3V battery do when it stores 4.8 x $10^-13$ C of charge on the plates of a capacitor.

   $W=\frac{1}{2}QV$
   $W=\frac{1}{2}(4.8\times{10^-13C})(3V)$
   $W=7.2\times{10^-13}J$

Example 8.2) A camera uses a 110uF capacitor to store energy for its flash. If the voltage across the capacitor is 330V, then how much energy is stored in the capacitor.

   $W=\frac{1}{2}CV^2$
   $W=\frac{1}{2}({110^-6F})\times(330V^2)$
   $W=6.0J$

Example 8.3) An AED uses 300J of electrical energy to shock a human heart back to normal rhythym. The energy is stored in a capacitor that is charged by a 5000V supply. (a) What capacitance is required to store this energy? (b) How much charge is stored on the plates?

   $W=\frac{1}{2}CV^2$
   $C=\frac{2W}{V^2}$
   $C=\frac{2(300J)}{(5000V)^2}$
   $C={2.4}\times{10^-5}F=24\mu{F}$ {Answer for (a)}
   $Q=CV$
   $Q=2.4\times{10^-5}(5000V)=0.120C$

Capacitors (9 of 9) Graphical Determination of Capacitance

Capacitor calculations - Basic calculations for capacitors in series and parallel

Charge, Capacitance and Energy

Formula to determine the amount of Charge stored in a Capacitor is,

$Charge(Coulombs,C)={Capacitance(Farad,F)\times{Voltage,(Volt,V)}$
$C=F\times{V}$

Example 1: For a capacitor rated at 1000uF and 16V has a Charge of,
C = 0.001F x 12 V = 0.012 Coulombs

Formula to determine the Capacitance of a Capacitor is,

$Capacitance(Farad,F)=\frac{Charge(Coulomb,C)}{Voltage,(Volt,V)}$
$F=\frac{C}{V}$

Example 2: The Capacity needed for the capacitor for the charge 0.000204 Coulombs at 12V is,
Capacity (F) = 0.000204C / 12 V = 0.000017 Farads (17uF)

Formula to determine the Energy stored in a Capacitor is,

$Energy(Joules,J)=0.5\times{Capacity(Farad,F)\times{Voltage^2,(Volt,V)}$
$J=0.5\times{F}\times{V^2}$

Example 3: The Stored Energy of the capacitor for the capacity 1000uF at 12V is,
J = 0.5 x 0.001F x (12x12)
= 0.072 Joules

Capacitor in Parallel and Series

Formula of Total Capacitance for Capacitors connected in Parallel is,

$Capacitance\underset{total}{}(C\underset{parallel}{})={C\underset{1}{}+C\underset{2}{}+C\underset{n}{}}$

Example 4: The total capacitance of three capacitors with capacity 1000uF, 330uF & 680uF (connected in Parallel) at 12V is,
$Capacitance\underset{total}{}(C\underset{parallel}{})={1000\mu{F}\underset{1}{}+330\mu{F}\underset{2}{}+680\mu{F}\underset{3}{}}$
= 2010uF

Formula of Total Charge for Capacitors connected in Parallel is,

$Charge\underset{total}{}={Capacitance\underset{total}{}+Voltage}$

Example 5: The total Charge of three capacitors (C1, C2, C3) with capacity 1000uF, 330uF & 680uF respectively, (connected in Parallel) at 12V is,
$Charge\underset{total}{}{}={0.00201{F}\times{12V}}$
= 0.02412 Coulombs

Example 6: The individual Charge of three capacitors (C1, C2, C3) with capacity 1000uF, 330uF & 680uF respectively, (connected in Parallel) at 12V is,
   $Charge\underset{C1}{}{}={0.001{F}\times{12V}}=0.012Coulombs$
   $Charge\underset{C2}{}{}={0.00033{F}\times{12V}}=0.00396Coulombs$
   $Charge\underset{C3}{}{}={0.00068{F}\times{12V}}=0.00816 Coulombs$

Formula of Total Capacitance for Capacitors connected in Series is,

$Capacitance\underset{total}{}(C\underset{series}{})={\frac{1}{\frac{1}{C\underset{1}{}}+\frac{1}{C\underset{2}{}}+\frac{1}{C\underset{n}{}}}}$

Example 7: The total Capacitance of three capacitors (C1, C2, C3) with capacity 1000uF, 330uF & 680uF respectively, (connected in Series) 12V is,
$Capacitance\underset{total}{}(C\underset{series}{})={\frac{1}{\frac{1}{1000\mu{F}\underset{1}{}}+\frac{1}{330\mu{F}\underset{2}{}}+\frac{1}{680\mu{F}\underset{3}{}}}}$
= 181.789uF

Example 8: The total Charge of three capacitors (C1, C2, C3) with capacity 1000uF, 330uF & 680uF respectively, (connected in Series) 12V is,
$Charge\underset{total}{}={0.000181F\underset{total}{}\times{12V}}$
= 0.002172Coulombs

Example 9: The individual Charge of three capacitors (C1, C2, C3) with capacity 1000uF, 330uF & 680uF respectively, (connected in Series) 12V is same as Total as they hold same amount of charge,
$Charge\underset{total}{}={0.000181F\underset{total}{}\times{12V}}$
= 0.002172Coulombs

Example 10: The individual Voltage of three capacitors (C1, C2, C3) with capacity 1000uF, 330uF & 680uF respectively, (connected in Series) 12V will be different as below,
   $Voltage,(Volt,V)=\frac{Charge(Coulomb,C)}{Capacitance(Farad,F)}$
   $V=\frac{C}{F}$
   $V\underset{C1}{}=\frac{0.002172}{0.001}=2.172Volts$
   $V\underset{C2}{}=\frac{0.002172}{0.00033}=6.582Volts$
   $V\underset{C3}{}=\frac{0.002172}{0.00068}=3.194Volts$
   $V\underset{total}{}=V\underset{C1}{}+V\underset{C2}{}+V\underset{C3}{}=11.948Volts\approx{12Volts}$

Capacitor Charge time is,

$TimeConstant={Resistance\underset{Ohm}{}}\times{Capacity\underset{Farad}{}}$

Example 11: Charge time of capacitor with capacity 1000uF at 12V, connected in Series with a 10kOhms resistor is,
$TimeConstant={10000\Omega}\times{0.001F}=10s$
5 x Time Constant = 5 x 10s = 50s to fully charge the 1000uF capacitor with 10kOhms resistor in series connection.

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Basic Electronics - Capacitance & Capacitors

Capacitors (1 of 9) What is a Capacitor, An Explanation Capacitance of a Capacitor, Where, -> Capaci...

Capacitors (1 of 9) What is a Capacitor, An Explanation

Capacitance of a Capacitor,

Capacitors (2 of 9) What is Capacitance? An Explanation

Capacitance of a Capacitor,

Capacitors (3 of 9) What is a Farad? An Explanation

Unit of Capacitance, Farad,

Capacitors (4 of 9) Calculating the Capacitance of a Capacitor, An Explanation

Calculating Capacitance of a Capacitor, Examples,

Capacitors (5 of 9) Calculating the Capacitance of a Capacitor, Worked Examples

Calculating Capacitance of a Capacitor, Examples,

Capacitors (6 of 9) Factors Affecting the Capacitance of a Capacitor

Factors affecting Capacitance of a Capacitor,

Capacitors (7 of 9) Energy Stored in a Capacitor, An Explanation

Energy Stored in a Capacitor,

Capacitors (8 of 9) Energy Stored in a Capacitor, Example Problems

Calculating Capacitance of a Capacitor, Examples,

Capacitors (9 of 9) Graphical Determination of Capacitance

Capacitor calculations - Basic calculations for capacitors in series and parallel

Charge, Capacitance and Energy

Formula to determine the amount of Charge stored in a Capacitor is,

Formula to determine the Capacitance of a Capacitor is,

Formula to determine the Energy stored in a Capacitor is,

Capacitor in Parallel and Series

Formula of Total Capacitance for Capacitors connected in Parallel is,

Formula of Total Charge for Capacitors connected in Parallel is,

Formula of Total Capacitance for Capacitors connected in Series is,

Capacitor Charge time is,

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