*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 R_{s} = R_{1} + R_{2} + R_{3} + ....

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

2. Parallel:

a. For resistors in parallel, the equivalent
resistance is 1/R_{p} = 1/R_{1} +1/R_{2} +1/R_{3}
+ ....

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