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?
a. For resistors in series, the equivalent resistance is Rs = R1 + R2 + R3 + ....
b. What physical quantity do series resistors have in common?
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.
Text Ch. 28: 14, 38, 43