Charging and Discharging of Capacitor

It's time to Know about Charging and Discharging of Capacitor

Capacitor

Charging Of A Capacitor :

Consider a series RC network connected to a battery of voltage 'V' through a switch 'S' . Let us assume that the Capacitor initially uncharged. There is no current when switch'S' is opened.

If the Switch is closed at t=0 there will be a current through resistor and Capacitor will begin to charge . Note that during charging process the charge transfered from one place to other through the resistor , switch and battery untill the Capacitor is fully charged . The maximum Charge depends upon the EMF the battery . Once the maximum charge is reached the current in the circuit is zero. Suppose at any instant during charging the circuit current is 'I' and Charge on the Capacitor is 'q' 

Applying Kirchoff's Voltage law 

V-IR-q/C = 0

RC series Circuit

Initial Current :

At t=0 when the Switch is closed , the charge on the Capacitor is zero therefore the current is maximum (I0) and is given by

I0 = V/R -------------------at t=0

Charge on the Capacitor at any instant during charging :

The charge 'q' at any time during charging can be shown to be 

q = Q(1-e^[-t/RC])
                             Q= Max Charge on capacitor = CV
Time constant  て = RC

q= Q(1-[e^(-t/て)])

Charging of capacitor

Voltage across capacitor at any instant during charging :

It can be shown mathematically that Voltage 'v' across capacitor at any time during charging is given by

v =  V(1-e^[-t/て])
V = final Voltage

Discharging of a Capacitor :

Consider the circuit I) consisting of a capacitor with an initial Charge "Q" , a resistor R and a switch "S" when the Switch is open. There is a potential difference  of Q/C across the Capacitor and zero potential difference across the resistor since I=0

Discharging of Capacitor

If the Switch is closed at t=0 the Capacitor begins to discharge through the resistor . At the same time during Discharging . Let Circuit current be I and Charge on capacitor  "q" . According to Kirchoff's Voltage Law potential drop across resistor = (IR) must be equal to potential difference across the Capacitor = (q/C)

IR = q/C

However the current in the circuit must be equal to the rate of decrease of charge on the Capacitor 

I.e  I = -dq/DT

Therefore 

This we see that both the charge on the Capacitor and the circuit current delay exponentially at a rate determined by the time constant て=RC

Discharging of Capacitor

20 Electrical Multiple Choice Questions

Hello all it's time to post 20 Electrical Multiple Choice Questions .......

Electrical MCQ 

Electrical engineering 20 MCQ :

1) If two capacitance​s C1 and C2 are connected in Parallel then the equivalent capacitance is given by

a) C1C2
b) C1/C2
c) C1C2/C1+C2
d) C1+C2

2) A resistor is connected across a 50 V Source. the current in the resistor if the color code is red,orange,silver is

a) 2mA
b)2.2mA
c)214mA
d)21.4 mA

3) Electrical Resistivity "r" is 

a) Low for copper & high for alloy
b)High for copper and low for alloy
c)Low for copper as well as for alloy
d) High for copper as well as for alloy

4) The rate of change of current in a 4H inductor is 2 Amps/sec Find the value of the voltage across the inductor

a) 8V
b) 0.8 V
c) 2V
d) 16 V

5) A linear circuit is one whose Parameters 

a) change with change in current
b) change with change in Voltage
c) do not change with voltage and current
d)none of the above

6) An active element in a circuit is one which 

a) Supplies the energy
b) Receives the energy
c) dissipate energy
d) both receives and supplies the energy

7)  Thevinins theorem cannot be applied to


a) active circuit
b) linear circuit
c) nonlinear circuit
d) passive circuit

8) If number of turns of a coil is increased it's inductance

a) remains the same
b)is increased
c) is decreased
d) none of the above

9) The unit of permeability is

a) WB/At ×m
b) At/m
c)At/WB
d) WB

10) The area of the hysteresis loop will be least for the following material is

a) wrought iron
b) hard steel
c) silicon steel
d) soft iron

11) If in An RLC series circuit , the frequency is below the resunant frequency then

a) XL=Xc
b) Xc<XL
c) Xc>XL
d) None of the above

12) Creeping in a single phase Induction type energy meter may be due to

a) over compensation for friction
b) over voltage
c) vibrations
d) all of the above

13) Which instrument is used to measure the high resistance

a) Kelvins Doubble bridge
b) Wheat Stone Bridge
c) Carey-Foster Bridge
d) Megger

14) The no load input power to a transformer is practically equal to 

a) Iron loss
b) Copper Loss
c) Eddy Current Loss
d) Windage loss

15) Which of the following motor is used in mixers?

a) Repulsion Motor
b) reluctance motor
c) hysteresis motor
d) universal motor



16)  which of the following fault come under the symmetrical faulta

a) LG fault
b) LL fault
c) LLG fault
d) LLLG fault

17) The acceptable grounding resistance for the domestic appliances is

a) 0.5 ohm
b) 1ohm
c) 1.5 ohm
d) 2 ohm


18) Which of the following motor is not self starting

a) Squrriel cage Induction Motor
b) Slip Ring Induction Motor
c) Synchronous Motor
d) Dc series motor

19)  If the power factor is high then the consumer maximum KVA demand 

a) increases
b) decreased 
c) Remains the same
d)  becomes zero

20) An amplifier has a gain of 10,000 expressed in decibels the gain is 

a) 10
b) 40
c) 80
d) 100

Please Comment Below If any one is wrong answers

Energy stored in the Capacitor & Energy Density

I am here now to discuss about the Energy stored in Capacitor

Capacitor

Energy Stored In a Capacitor :

Consider a parallel plate Capacitor it initially uncharged so that the initial potential difference across the plates is zero

Now imagine that the Capacitor is connected to a battery which develops a maximum charge "q" and a final potential across the plates is "V" 
Since the Capacitor is charged linearly the q-V graph is straight line passing through the origin

q-V Characteristics

Since the initial potential difference is zero, the average potential difference during the charging process

= (0+V)
= V/2

Energy Stored  U = V/2 ×q = 1/2 qV


The energy stored in the Capacitor can be expressed in alternate forms

•It is clear from the above expression that energy stored increases with increase of potential difference.



Energy Density :


The energy stored in the Capacitor can be considered as being stored in the Electric field created between the plates as the Capacitor is charged 

Consider a parallel plate Capacitor with  Area of Plate "A" and separation "d" 

Parallel plate Capacitor

Energy stored 
U = 1/2 CV^2

The energy stored per unit volume is called energy Density (u) since the volume of parallel plate is 'Ad'

Therefore energy Density ( i.e Electric field energy stored per unit volume ) in any region of space is directly proportional to the square of the Electric field Intensity in the region

Related Links :

Capacitor & Capacitance
Capacitance of parallel plate Capacitor

Capacitance of parallel plate Capacitor & Dielectric Constant & Dielectric Strength of Capacitor

Hello all here is another post about the Capacitor

Capacitor

Capacitance of a parallel plate Capacitor :

Parallel plate Capacitor
1) air as Dielectric 2) some other Dielectric medium

The figure shows a parallel plate air capacitor is given by 


Cair = ε0 A/d


Where  A is the area of each plate
          d is the plate separation


It is clear that capacitance of a parallel plate Capacitor is directly proportional to the area of plates and inversily proportional to plate separation

When space between plates completely filled with Dielectric the capacitance of capacitor is given by

Cm = εA/d
     = ε0εrA/d
     =εr Cair

Dielectric Constant of capacitor :

Capacitance of a parallel plate air Capacitor is Given by

Cair = ε0A/d


If the space between the plates completely filled with a Dielectric of relative Permittivity "εr" then the capacitance of capacitor is given by

Cm = εr Cair

Cm/Cair = εr


Dielectric Strength :

The maximum value of Electric field Intensity ( i.e potential gradient ) that can be applied to a Dielectric without it's Electric breakdown is called Dielectric strength of the Dielectric .

Related Topics :

Capacitor And Capacitance 

Electric field Intensity


Please Comment Below If You Have Any Suggestions Or Doubts

Capacitor And Capacitance

Capacitor :

Capacitor

A Capacitor is a device that is capable of storing charge. It essentially consists of two conducting surfaces separated by an insulating material.

The conducting surfaces are called plates of the capacitor and the insulating material is called Dielectric.
The most commonly used dielectrics are air,mica,paper etc

• A capacitor is generally named after the Dielectric used e.g air capacitor, mica capacitor, paper capacitor etc
• The capacitor may be in the form of parallel plates  (parallel plate capacitor ), concentric cylinders ( cylindrical capacitor ) or other arrangements

Capacitance :

Parallel plate capacitor connected to battery

The ability of a capacitor to share Charge is known as it's capacitance

Consider a parallel plate air capacitor connected to a battery. The  electrons from plate 'A' attracted by the battery and these electrons start pilling upon plate 'B' . This action is reffered as the charging of the capacitor because capacitor plates are being charged. It has been found experimentally that charge 'q' stored in a capacitor is directly proportional to the p.d (V) across the plates  i.e

q∝ V

q/V =Constant = C

The constant of proportionality C is called capacitance of capacitor . The unit of capacitance is farad

1 C/V = 1 farad

• By definition capacitance is always a positive quantity
• The p.d across the capacitor increases linearly with increase of Charge on the capacitor plate there fore the ratio q/V is constant for a given capacitor

CAPACITOR & CAPACITANCE

Lets know about Capacitor Because Capacitor is a important Element in The Electrical Basics

◆Capacitor :

A capacitor essentially consists of two conducting surfaces separated
by a layer of an insulating medium called dielectric. The conducting surfaces may be in the form of either circular (or rectangular) plates or be of
spherical or cylindrical shape. The purpose of a capacitor is to store electrical energy by electrostatic stress in the dielectric (the word ‘condenser’
is a misnomer since a capacitor does not ‘condense’ electricity as such, it
merely stores it).
A parallel-plate capacitor is shown in Fig. One plate is joined to
the positive end of the supply and the other to the negative end or is earthed.
It is experimentally found that in the presence of an earthed plate B, plate
A is capable of withholding more charge than when B is not there. When
such a capacitor is put across a battery, there is a momentary flow of
electrons from A to B. As negatively-charged electrons are withdrawn
from A, it becomes positive and as these electrons collect on B, it becomes
negative. Hence, a p.d. is established between plates A and B. The transient
flow of electrons gives rise to charging current. The strength of the charging
current is maximum when the two plates are uncharged but it then decreases and finally ceases when

p.d. across the plates becomes slowly and slowly equal and opposite to the battery e.m.f.

◆Capacitance :

The property of a capacitor to ‘store electricity’ may be called
its capacitance.
As we may measure the capacity of a tank, not by the total
mass or volume of water it can hold, but by the mass in kg of
water required to raise its level by one metre, similarly, the
capacitance of a capacitor is defined as “the amount of charge
required to create a unit p.d. between its plates.”
Suppose we give Q coulomb of charge to one of the two plate
of capacitor and if a p.d. of V volts is established between the two,
then its capacitance is
 C = Q/V


Capacitance = Charge/Potential Difference


Hence, capacitance is the charge required per unit potential difference.
By definition, the unit of capacitance is coulomb/volt which is also called farad (in honour of
Michael Faraday)
∴ 1 farad = 1 coulomb/volt


One farad is defined as the capacitance of a capacitor which requires a charge of one coulomb
to establish a p.d. of one volt between its plates.
One farad is actually too large for practical purposes. Hence, much smaller units like microfarad
(μF), nanofarad (nF) and micro-microfarad (μμF) or picofarad (pF) are generally employed.

1 μF = 10−9 F; 1 nF = 10−9 F ; 1 μμF or pF = 10−12F


Incidentally, capacitance is that property of a capacitor which delays and change of voltage
across it.