# Transient Behavior of Capacitor

At the beginning, this current will be maximum and after certain time the current will become zero. The duration in which current changes in capacitor is known as transient period. The phenomenon of charging current or other electrical quantities like voltage, in capacitor is known as transient.

To understand **transient behavior of capacitor** let us draw a RC circuit as shown below,
Now, if the switch S is suddenly closed, the current starts flowing through the circuit. Let us current at any instant is i(t).

Also consider the voltage developed at the capacitor at that instant is V_{c}(t).
Hence, by applying Kirchhoff’s Voltage Law, in that circuit we get,
Now, if transfer of charge during this period (t) is q coulomb, then
i(t) can be written as
Therefore,
Putting this expression of i(t) in equation (i) we get,
Now integrating both sides with respect to time we get,
Where, K is a constant can be determined from initial condition.

Let us consider the time t = 0 at the instant of switching on the circuit putting t = 0 in above equation we get,
There will be no voltage developed across capacitor at t = 0 as it was previously unchanged.

Therefore,
Now if we put RC = t at above equation, we get
This RC or product of resistance and capacitance of RC series circuit is known as time constant of the circuit. So, time constant of an RC circuit, is the time for which voltage developed or dropped across the capacitor is 63.2% of the supply voltage. This definition of time constant only holds good when the capacitor was initially unchanged.

Again, at the instant of switching on the circuit i.e. t = 0, there will be no voltage developed across the capacitor. This can also be proved from equation (ii).
So initial current through the circuit is, V/R and let us consider it as I_{0}.

Now at any instant, current through the circuit will be,
Now when, t = Rc the circuit current.
So at the instant when, current through the capacitor is 36.7% of the initial current, is also known as time constant of the RC circuit.

The time constant is normally denoted will τ (taw). Hence,

## Transient During Discharging a Capacitor

Now, suppose the capacitor is fully charged, i.e. voltage at capacitor is equal to the voltage of source. Now if the voltage source is disconnected and instead two terminals of the battery are short circuited, the capacitor will stared discharging means, unequal distribution of electrons between two plates will be equalized through the short circuit path. The process of equaling electrons concentration in two plates will continue until the voltage at capacitor becomes zero. This process is known as discharging of capacitor. Now we will examine the**transient behavior of capacitor**during discharging. Now, from the above circuit by applying Kirchhoff Current Law, we get, Integrating both sides we get, K is the constant which can be determined from initial value. Now, at the time of short circuiting the capacitor, Now, from equation (iii), by applying t = τ = RC we get, Again, circuit current at that time i.e. τ = RC, Thus at time constant of capacitor, both capacitor voltage, ϑ

_{c}and current i are reduced to 36.8 % of their initial value.

**Comments/Feedbacks**

Closely Related Articles Working Principle of a CapacitorQuality Factor of Inductor and CapacitorCylindrical CapacitorSpherical CapacitorCapacitors in Series and ParallelHow to Test Capacitors?More Related Articles Electric Current and Theory of Electricity | Heating and Magnetic EffectNature of ElectricityDrift Velocity Drift Current and Electron MobilityElectric Current and Voltage Division RuleRMS or Root Mean Square Value of AC SignalElectrical Conductance Conductivity of Metal Semiconductor and Insulator | Band TheoryWhat is Electrical Resistance?Resistivity and Laws of ResistanceProperties of Electric ConductorTemperature Coefficient of ResistanceResistance Variation with TemperatureSeries ResistanceActive and Passive Elements of Electrical CircuitElectrical DC Series and Parallel CircuitOhm's Law | Equation Formula and Limitation of Ohm's LawKirchhoff Current Law and Kirchhoff Voltage LawSingle and Multi Mesh AnalysisSuperposition TheoremThevenin Theorem and Thevenin Equivalent Voltage and ResistanceNorton Theorem | Norton Equivalent Current and ResistanceReciprocity TheoremNodal Analysis in Electric CircuitsMaximum Power Transfer TheoremDelta - Star transformation | Star - Delta TransformationMagnetic FieldMagnetic FluxMagnetic PermeabilityHysteresis LoopMagnetic Field and Magnetic Circuit | Magnetic MaterialsMagnetic SaturationEnergy Stored in a Magnetic FieldStatic Electric Field | Electrostatic Induction A Current Carrying Conductor Within A Magnetic FieldMagnetic SusceptibilityHard Magnetic MaterialsSoft Magnetic MaterialsMagnetic Circuit with Air GapElectric ChargeCoulombs Law | Explanation Statement Formulas Principle Limitation of Coulomb’s LawElectric Lines of ForceWhat is Electric Field?Electric Field Strength or Electric Field IntensityWhat is Flux? Types of Flux?Electric FluxElectric PotentialCapacitor and Capacitance | Types of CapacitorsEnergy Stored in CapacitorCharging a CapacitorDischarging a CapacitorFourier Series and Fourier TransformTrigonometric Fourier SeriesAnalysis of Exponential Fourier SeriesParity GeneratorElectric Circuit and Electrical Circuit ElementsSeries Parallel Battery CellsRL Series CircuitWhat is Inductor and Inductance | Theory of InductorRLC CircuitThree Phase Circuit | Star and Delta SystemRL Parallel CircuitRL Circuit Transfer Function Time Constant RL Circuit as FilterConstruction of AC Circuits and Working of AC CircuitsSeries RLC CircuitParallel RLC CircuitResistances in Series and Resistances in ParallelResonance in Series RLC CircuitPlanar and Non Planar Graphs of CircuitClipping CircuitMutual InductanceSelf InductanceSI System of UnitsElectrical International SymbolElectric Power Single and Three Phase Power Active Reactive ApparentVector Algebra | Vector DiagramRelationship of Line and Phase Voltages and Currents in a Star Connected SystemVector Diagram | Three Phase Vector DiagramTypes of Resistor Carbon Composition and Wire Wound ResistorVaristor Metal Oxide Varistor is Nonlinear ResistorCarbon Composition ResistorWire Wound ResistorVariable Resistors | Defination, Uses and Types of Variable ResistorsLight Dependent Resistor | LDR and Working Principle of LDRSource of Electrical EnergyVoltage SourceIdeal Dependent Independent Voltage Current SourceVoltage or Electric Potential DifferenceVoltage in SeriesVoltage in ParallelVoltage Drop CalculationVoltage DividerVoltage MultiplierVoltage DoublerVoltage RegulatorVoltage FollowerVoltage Regulator 7805Voltage to Current ConverterNew Articles Principle of Water Content Test of Insulating OilCollecting Oil Sample from Oil Immersed Electrical EquipmentCauses of Insulating Oil DeteriorationAcidity Test of Transformer Insulating OilMagnetic Flux