Capacitor and Inductor

Capacitor

Conceptually a capacitor is composed of a pair of plates of conductor which can be charged by a voltage source. The voltage between the two plates is proportional to the charge $Q$, but inversely proportional to the capacity $C$ of the capacitor:

$$V=\frac{Q}{C}$$

Inductor

• Electromagnetic Interaction: Electricity to Magnetism

  Magnetic field (flux) is generated in the space around a current flowing through a piece of conductor:

  The magnetic field around a coil is the superposition of the magnetic flux generated by each section of the coil:

• Electromagnetic Interaction: Magnetism to Electricity

  Electric current is induced in a conductor when there is changing magnetic flux in the surrounding space.

  

• Self and Mutual Induction

  A time-varying electric current in a coil will cause a time-varying magnetic field in the surrounding space, which in turn will induce electric voltage and then current in the same coil (self-induction) or a different coil in the neighborhood (mutual-induction).

• Faraday's Law:

  The self-induced voltage across the coil due to a current $i(t)$ is proportional to the rate of change over time of the total magnetic flux caused by the current:
  

  $$v(t)=\frac{d\Psi(t)}{dt}=N\frac{d\Phi(t)}{dt}=L\frac{di(t)}{dt}$$
  
  
  Here $\Psi=N\Phi=Li$ is the total magnetic flux in the coil, and $L=\Psi/i$ is the inductance of the coil that represents how much flux can be generated by the coil per unit current.

• Lenz's Law:

  The polarity of the self-induced voltage $v(t)$ in a coil is such that it tends to produce a current which induces a magnetic flux to oppose the change of the magnetic field that induced the voltage, thereby opposing any change in current $i(t)$ that is causing the magnetic flux.

  When current $i(t)$ increases, the induced voltage $v(t)$ tends to resist it, when current $i(t)$ decreases, the induced voltage $v(t)$ tends to sustain it.