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By the end of the section, you will be able to:
  • Describe the charging process of a capacitor
  • Describe the discharging process of a capacitor
  • List some applications of RC circuits

When you use a flash camera, it takes a few seconds to charge the capacitor that powers the flash. The light flash discharges the capacitor in a tiny fraction of a second. Why does charging take longer than discharging? This question and several other phenomena that involve charging and discharging capacitors are discussed in this module.

Circuits with resistance and capacitance

An RC circuit    is a circuit containing resistance and capacitance. As presented in Capacitance , the capacitor is an electrical component that stores electric charge, storing energy in an electric field.

[link] (a) shows a simple RC circuit that employs a dc (direct current) voltage source ε , a resistor R , a capacitor C , and a two-position switch. The circuit allows the capacitor to be charged or discharged, depending on the position of the switch. When the switch is moved to position A , the capacitor charges, resulting in the circuit in part (b). When the switch is moved to position B , the capacitor discharges through the resistor.

Part a shows an open circuit with three branches, left branch is a voltage source with upward positive terminal connected to point A, the middle branch is a short circuit with point B and right branch is a resistor with a capacitor. Part b shows circuit of part a with first branch connected to third branch. Part c shows circuit of part a with second branch connected to third branch.
(a) An RC circuit with a two-pole switch that can be used to charge and discharge a capacitor. (b) When the switch is moved to position A , the circuit reduces to a simple series connection of the voltage source, the resistor, the capacitor, and the switch. (c) When the switch is moved to position B , the circuit reduces to a simple series connection of the resistor, the capacitor, and the switch. The voltage source is removed from the circuit.

Charging a capacitor

We can use Kirchhoff’s loop rule to understand the charging of the capacitor. This results in the equation ε V R V c = 0 . This equation can be used to model the charge as a function of time as the capacitor charges. Capacitance is defined as C = q / V , so the voltage across the capacitor is V C = q C . Using Ohm’s law, the potential drop across the resistor is V R = I R , and the current is defined as I = d q / d t .

ε V R V c = 0 , ε I R q C = 0 , ε R d q d t q C = 0.

This differential equation can be integrated to find an equation for the charge on the capacitor as a function of time.

ε R d q d t q C = 0 , d q d t = ε C q R C , 0 q d q ε C q = 1 R C 0 t d t .

Let u = ε C q , then d u = d q . The result is

0 q d u u = 1 R C 0 t d t , ln ( ε C q ε C ) = 1 R C t , ε C q ε C = e t R C .

Simplifying results in an equation for the charge on the charging capacitor as a function of time:

q ( t ) = C ε ( 1 e t R C ) = Q ( 1 e t τ ) .

A graph of the charge on the capacitor versus time is shown in [link] (a). First note that as time approaches infinity, the exponential goes to zero, so the charge approaches the maximum charge Q = C ε and has units of coulombs. The units of RC are seconds, units of time. This quantity is known as the time constant :

τ = R C .

At time t = τ = R C , the charge is equal to 1 e −1 = 1 0.368 = 0.632 of the maximum charge Q = C ε . Notice that the time rate change of the charge is the slope at a point of the charge versus time plot. The slope of the graph is large at time t = 0.0 s and approaches zero as time increases.

Questions & Answers

The properties of a system during a reversible constant pressure non-flow process at P= 1.6bar, changes from constant volume of 0.3m³/kg at 20°C to a volume of 0.55m³/kg at 260°C. its constant pressure process is 3.205KJ/kg°C Determine: 1. Heat added, Work done, Change in Internal Energy and Change in Enthalpy
Opeyemi Reply
please how do dey get 5/9 in the conversion of Celsius and Fahrenheit
Gwam Reply
what is copper loss
timileyin Reply
this is the energy dissipated(usually in the form of heat energy) in conductors such as wires and coils due to the flow of current against the resistance of the material used in winding the coil.
Henry
it is the work done in moving a charge to a point from infinity against electric field
Ashok Reply
what is the weight of the earth in space
peterpaul Reply
As w=mg where m is mass and g is gravitational force... Now if we consider the earth is in gravitational pull of sun we have to use the value of "g" of sun, so we can find the weight of eaeth in sun with reference to sun...
Prince
g is not gravitacional forcé, is acceleration of gravity of earth and is assumed constante. the "sun g" can not be constant and you should use Newton gravity forcé. by the way its not the "weight" the physical quantity that matters, is the mass
Jorge
Yeah got it... Earth and moon have specific value of g... But in case of sun ☀ it is just a huge sphere of gas...
Prince
Thats why it can't have a constant value of g ....
Prince
not true. you must know Newton gravity Law . even a cloud of gas it has mass thats al matters. and the distsnce from the center of mass of the cloud and the center of the mass of the earth
Jorge
please why is the first law of thermodynamics greater than the second
Ifeoma Reply
define electric image.obtain expression for electric intensity at any point on earthed conducting infinite plane due to a point charge Q placed at a distance D from it.
Mateshwar Reply
explain the lack of symmetry in the field of the parallel capacitor
Phoebe Reply
pls. explain the lack of symmetry in the field of the parallel capacitor
Phoebe
does your app come with video lessons?
Ahmed Reply
What is vector
Ajibola Reply
Vector is a quantity having a direction as well as magnitude
Damilare
tell me about charging and discharging of capacitors
Ahemen Reply
a big and a small metal spheres are connected by a wire, which of this has the maximum electric potential on the surface.
Bundi Reply
3 capacitors 2nf,3nf,4nf are connected in parallel... what is the equivalent capacitance...and what is the potential difference across each capacitor if the EMF is 500v
Prince Reply
equivalent capacitance is 9nf nd pd across each capacitor is 500v
santanu
four effect of heat on substances
Prince Reply
why we can find a electric mirror image only in a infinite conducting....why not in finite conducting plate..?
Rima Reply
because you can't fit the boundary conditions.
Jorge
what is the dimensions for VISCOUNSITY (U)
Branda
Practice Key Terms 1

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Source:  OpenStax, University physics volume 2. OpenStax CNX. Oct 06, 2016 Download for free at http://cnx.org/content/col12074/1.3
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