Chapter 14- Circuits

Capacitance

• A capacitor is a device that can store energy in an electric field

• It is a little like a battery, but only stores, does not ‘produce’ electrons. Also, a capacitor can ‘dump’ it’s charge very quickly, whereas a battery takes a while

  

• Can consist of 2 conductors of any shape placed near each other without touching

• The region between them is commonly filled with an electrically insulating material called a dielectric which will increase the electric field

• The material will dictate what the capacitor will be used for

  

• The charge collects on the metallic plates, and

  • one becomes positively charged (loses e-)

  • one becomes negatively charged (gains e-)

• Molecules in the dielectric material become polarized

  

• Image the capacitor as a water tower hooked to a pipe. The water tower ‘stores’ water pressure—when the water system pumps produce more water than a town needs, the excess is stored in the tower. Then, at times of high demand, the excess water flows out of the tower to keep pressure up. A capacitor stores electrons in the same way and can release them later

• The equation depends on the area of the two plates, the composition of the dielectric, and the distance between the two plates

  C = kε_oA / d = εA / d

  • ε is the permitivity of the dielectric (insulating) material and is made up of k times ε_o where k is the relative permitivity and ε_o is 8.854×10^-12 F/m

    • k = 1 unless told otherwise!

• The amount of charge is related to the potential difference; this ratio is the capacitance

  Q = CV or C = Q / V

  • where Q is the charge (in Coulombs, C)

  • where V is the voltage (in Volts, V)

  • where C is the capacitance (in Farads, f)

    • 1 farad = 1 Coulomb / Volt

      • many times the μF is used (microfarad) - x 10^-6

• Because the capacitor stores charge, it also stores electrical energy

• The battery does ‘work’ transferring charge across the plates

  E = ½CV² or E= ½QV

• Circuits are diagrams that show us the wiring, power source, and whatever else might be connected by the wire

• They show us the pathway for electrons to travel

• For continuous flow, circuit must be complete with no gaps

• There are plenty of things that can be in a circuit

  

• Electrons flow into (+) or out of (-) the battery

  

• Capacitors can be in series or in parallel wiring of a circuit

  

• A single pathway for electron flow between terminals of a battery, generator, etc.

  • Any break will stop the flow

  • Since there is only one way for the charge to flow, the charge is the same everywhere

  • Voltage is kind of like the push to get it to go (like a toll booth)

• Capacitors in series all have the same charge; the total voltage is the sum of the voltages across each capacitor

  

• In parallel wiring, branches are formed, each of which is a separate path for the flow of electrons

  • Electrons will only travel through one way (1 branch), so charge is divided

  • Each branch is independent of another, so a break in one does not interrupt total flow

• Capacitors in parallel all have the same potential difference; the total charge

  

• We can picture capacitors in parallel as forming one capacitor with a larger area