capacitor

Examples of capacitor in the following topics:

• Combinations of Capacitors: Series and Parallel

  • These combinations can be in series (in which multiple capacitors can be found along the same path of wire) and in parallel (in which multiple capacitors can be found along different paths of wire).
  • Total capacitance for a circuit involving several capacitors in parallel (and none in series) can be found by simply summing the individual capacitances of each individual capacitor .
  • This image depicts capacitors C1, C2, and so on until Cn in parallel.
  • This image depicts capacitors C1, C2 and so on until Cn in a series.
  • Calculate the total capacitance for the capacitors connected in series and in parallel

• Capacitors with Dielectrics

  • A dielectric partially opposes a capacitor's electric field but can increase capacitance and prevent the capacitor's plates from touching.
  • The part near the positive end of the capacitor will have an excess of negative charge, and the part near the negative end of the capacitor will have an excess of positive charge .
  • On the other hand, the dielectric prevents the plates of the capacitor from coming into direct contact (which would render the capacitor useless).
  • The capacitance for a parallel-plate capacitor is given by:
  • Describe the behavior of the dielectric material in a capacitor's electric field

• Resistors and Capacitors in Series

  • An RC circuit has a resistor and a capacitor and when connected to a DC voltage source, and the capacitor is charged exponentially in time.
  • An RC circuit is one containing a resistor R and a capacitor C.
  • The capacitor is initially uncharged.
  • (a) An RC circuit with an initially uncharged capacitor.
  • Mutual repulsion of like charges in the capacitor progressively slows the flow as the capacitor is charged, stopping the current when the capacitor is fully charged and Q=C⋅emf.

• Parallel-Plate Capacitor

  • A capacitor is an electrical component used to store energy in an electric field.
  • Capacitors can take many forms, but all involve two conductors separated by a dielectric material.
  • For the purpose of this atom, we will focus on parallel-plate capacitors .
  • Charges in the dielectric material line up to oppose the charges of each plate of the capacitor.
  • An electric field is created between the plates of the capacitor as charge builds on each plate.

• Parallel-Plate Capacitor

  • One of the most commonly used capacitors in industry and in the academic setting is the parallel-plate capacitor .
  • This is a capacitor that includes two conductor plates, each connected to wires, separated from one another by a thin space.
  • The purpose of a capacitor is to store charge, and in a parallel-plate capacitor one plate will take on an excess of positive charge while the other becomes more negative.
  • The maximum energy (U) a capacitor can store can be calculated as a function of Ud, the dielectric strength per distance, as well as capacitor's voltage (V) at its breakdown limit (the maximum voltage before the dielectric ionizes and no longer operates as an insulator):
  • In a capacitor, the opposite plates take on opposite charges.

• Capacitance

  • The most common capacitor is known as a parallel-plate capacitor which involves two separate conductor plates separated from one another by a dielectric .
  • For a parallel-plate capacitor, this equation can be used to calculate capacitance:
  • In storing charge, capacitors also store potential energy, which is equal to the work (W) required to charge them.
  • For a capacitor with plates holding charges of +q and -q, this can be calculated:
  • In a parallel-plate capacitor, this can be simplified to:

• Capacitors in AC Circuits: Capacitive Reactance and Phasor Diagrams

  • The voltage across a capacitor lags the current.
  • For a circuit with a capacitor, the instantaneous value of V/I is not constant.
  • The capacitor is affecting the current, having the ability to stop it altogether when fully charged.
  • Since an AC voltage is applied, there is an rms current, but it is limited by the capacitor.
  • This is considered to be an effective resistance of the capacitor to AC, and so the rms current Irms in the circuit containing only a capacitor C is given by another version of Ohm's law to be $I_{rms} = \frac{V_{rms}}{X_C}$, where Vrms is the rms voltage.

• RLC Series Circuit: At Large and Small Frequencies; Phasor Diagram

  • We also learned the phase relationships among the voltages across resistor, capacitor and inductor: when a sinusoidal voltage is applied, the current lags the voltage by a 90º phase in a circuit with an inductor, while the current leads the voltage by 90∘ in a circuit with a capacitor.
  • When $Z \approx X_C$, the circuit is almost equivalent to an AC circuit with just a capacitor.
  • A series RLC circuit: a resistor, inductor and capacitor (from left).

• Phase Angle and Power Factor

  • Therefore we can say: the currents in the resistor and capacitor are equal and in phase.
  • On the other hand, because the total voltage should be equal to the sum of voltages on the resistor and capacitor, so we have:
  • As learned from the preceding series of Atoms—the voltage across the capacitor VC follows the current by one-fourth of a cycle (or 90º).
  • Compare the currents in the resistor and capacitor in a series RC circuit connected to an AC voltage source

• Impedance

  • Rather than solving the differential equation relating to circuits that contain resistors and capacitors, we can imagine all sources in the circuit are complex exponentials having the same frequency.
  • For a capacitor, $i = C \frac{dv}{dt}$.
  • The impedance of a resistor is R, while that of a capacitor (C) is $\frac{1}{j \omega C}$.