EMF AND CIRCUITS

I. Batteries and generators which are able to maintain a potential difference between two points and supply a flow of charge are called sources of electromotive force (emf)

  A. The convention for a current -> a flow of positive charge; current flows from a (+) terminal on a source of emf, through an external circuit, and arrives back at the (-) terminal of the emf source. Within the source of emf, the charge is then "pumped" from low potential to high potential. If there is an external resistance R and the emf has some internal resistance r, then the current

   I = (emf)/(R+r)










II. How is power produced and dissipated in a circuit that contains an source of emf and a single resistance R?








III. Circuits

  A. Resistors

   1. Series:

    a. For resistors in series, the equivalent resistance is Rs = R1 + R2 + R3 + ....






    b. What physical quantity do series resistors have in common?





   2. Parallel:

    a. For resistors in parallel, the equivalent resistance is 1/Rp = 1/R1 +1/R2 +1/R3 + ....

     

    b. What do resistors in parallel have in common?










  B. Kirchoff's Rules

   1. A branch point is a point where 3 or more conductors are joined.





    2. A loop is any closed conducting path.






    3. Point Rule: The algebraic sum of the currents toward any branch point is zero. [ (+) if toward and (-) if away]

    4. Loop Rule: The algebraic sum of the emf's and potential differences in any loop is zero.

  D. What happens if we form a circuit using a source of emf, a switch, a resistor, and a capacitor in series?

   1. We find that when the switch is closed, the charge builds up on the capacitor and the current is a function of time. Using     the loop rule we get

      (emf) - iR -q/C = 0

      where i and q are now time dependent. Using i = dq/dt, we can show that charging the capacitor takes some time and the       time dependence of the charge on the capacitor is

      q = C(emf)(1-e-t/RC)        

      where RC is called the time constant.







EXAMPLES

Text Ch. 28: 14, 38, 43