ONLINE ELECTRICAL ENGINEERING STUDY SITE

Charging a Capacitor

Whenever we connect an uncharged capacitor with a voltage source it is exponentially charged until the voltage developed across the capacitor becomes equal and opposite to voltage of the source.
Let us connect one capacitor of capacitance C in series with a resistor of resistance R. We also connect this series combination of capacitor and resistor with a battery of voltage V through a push switch S. charging a capacitor When we push the switch, the capacitor is uncharged, hence no voltage developed across the capacitor, thus the capacitor will behave as short circuit. The current through the circuit will only be limited by resistance R. That initial current is V / R. Now slowly the voltage is being developed across the capacitor, and this developed voltage is in opposite of the polarity of battery. As a result the current in the circuit gradually decreased. It will be gradually decreased to zero, when the voltage across the capacitor becomes equal and opposite of the voltage of battery.

The voltage is gradually increased across the capacitor during charging. Let us consider the rate of increase of voltage across the capacitor is dv/dt at any instant t. The current though the capacitor at that instant is Applying, Kirchhoff’s Voltage Law, in the circuit at that instant, we can write, Integrating both side we get, Now, at the time of switching on the circuit, voltage across the capacitor was zero. That means, v = 0 at t = 0. Putting these values in above equation, we get After getting the value of A, we can rewrite the above equation as, Now, we know that, This is the expression of charging current I, during process of charging. The current and voltage of the capacitor during charging is shown below. charging a capacitor




Comments/Feedbacks






Closely Related Articles Electric 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 CapacitorDischarging a CapacitorMore 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 SignalWorking Principle of a CapacitorQuality Factor of Inductor and CapacitorTransient Behavior of CapacitorCylindrical CapacitorSpherical CapacitorCapacitors in Series and ParallelHow to Test Capacitors?Electrical 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 GapFourier 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 Collecting Oil Sample from Oil Immersed Electrical EquipmentCauses of Insulating Oil DeteriorationAcidity Test of Transformer Insulating OilMagnetic FluxRing Counter