capacitance

Examples of capacitance in the following topics:

• Combinations of Capacitors: Series and Parallel

  • Like in the case of resistors in parallel, the reciprocal of the circuit's total capacitance is equal to the sum of the reciprocals of the capacitance of each individual capacitor :
  • 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 .
  • To find total capacitance of the circuit, simply break it into segments and solve piecewise .
  • With effectively two capacitors left in parallel, we can add their respective capacitances (c) to find the total capacitance for the circuit.
  • Calculate the total capacitance for the capacitors connected in series and in parallel

• Capacitance

  • Capacitance is the measure of an object's ability to store electric charge.
  • Capacitance is the measure of an object's ability to store electric charge.
  • Any body capable of being charged in any way has a value of capacitance.
  • For a parallel-plate capacitor, this equation can be used to calculate capacitance:
  • Express the relationship between the capacitance, charge of an object, and potential difference in the form of equation

• Capacitors with Dielectrics

  • A dielectric partially opposes a capacitor's electric field but can increase capacitance and prevent the capacitor's plates from touching.
  • If it has a high permittivity, it also increases the capacitance for any given voltage.
  • The capacitance for a parallel-plate capacitor is given by:

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

  • Response of an RLC circuit depends on the driving frequency—at large enough frequencies, inductive (capacitive) term dominates.
  • The impedance Z at small frequencies $(\nu \ll \frac{1}{\sqrt{2\pi LC}})$ is dominated by the capacitive term, assuming that the frequency is high enough so that XC is much larger than R.

• Parallel-Plate Capacitor

  • For a parallel-plate capacitor, capacitance (C) is related to dielectric permittivity (ε), surface area (A), and separation between the plates (d):

• Parallel-Plate Capacitor

  • Accordingly, capacitance is greatest in devices with high permittivity, large plate area, and minimal separation between the plates.

• Capacitors in AC Circuits: Capacitive Reactance and Phasor Diagrams

  • However, the value of Vmax/Imax is useful, and is called the capacitive reactance (XC) of the component.
  • The value of XC (C standing for capacitor) depends on its capacitance (C) and the frequency (f) of the alternating current.

• Impedance

  • Express the relationship between the impedance, the resistance, and the capacitance of a series RC circuit in a form of equation

• Resistors and Capacitors in Series

  • In terms of voltage, across the capacitor voltage is given by Vc=Q/C, where Q is the amount of charge stored on each plate and C is the capacitance.

• Exercises

  • where $q$ is the charge on the capacitor, $L$ is the inductance of the coil, $R$ is the resistance, $C$ the capacitance, and $V$ is the applied voltage.
  • (d) If the inductance is $25 \times 10 ^{-3}$ H (1 Henry = 1 volt per amp per second), what capacitance is required to have a characteristic period of 1 second?