Last time	Today	Fri.
Ch18.8, Ch19.2	Ch19.3-.5	Ch19.6-.7, and 19.9
Alternating currents, voltages, and power. EMF and terminal voltages.	Kirchoff's Laws, and associated problems.	Series and parallel capacitors. Capacitors and resistors in circuits.

Last time we worked on AC currents, voltages, and power. Also quickly looked at internal resistance of real batteries. Main points are:

, ,

1. Average power is half the peak power and equal to rms IV
2. Real batteries only provide some maximum current. We model the maximum current by including an internal resistance. Then, Imax=Vint/r.

Kirchoff's Laws.

We have been working circuit problems long enough now to be rather familiar with conservation of charge, conservation of energy, and Ohm's Law. At this point in the class, you should be comfortable with the use of parallel and series resistor laws to figure out currents through some complicated looking circuits. For example:

Example 1: Let's just quickly work through a parallel and series resistor problem. Think about the circuit shown below. What is the total current flowing through the circuit?

One way to do this problem is to calculate the parallel resistance and then use Ohm's Law. We find the two 100 Ohm resistors are like a 50 Ohm resistor. Then we parallel that with the other 50 Ohm resistor to get a parallel effective resistor of 25 Ohms. That across a 10 volt battery gives 0.4Amps.

As the circuits get more and more complicated, it becomes more difficult and eventually, for some circuits, impossible to figure them out using just series and parallel resistor rules. Kirchoff developed more general rules. They go like this:

1. Conservation of charge tells us that the sum of all the currents coming into some 'node' on a circuit must equal the sum of all the currents leaving the node.
2. Conservation of energy tells us that the sum of all the voltages around a closed loop in a circuit must be zero.

Together, these two rules can be used to work through circuit problems more quickly. For example, in the problem we just worked out, Kirchoff 2 shows us that all the resistors have the same voltage drop, and that it is equal to the battery voltage. Kirchoff 1 shows that the total current is just the sum of the currents of 0.1A+0.1A+0.2A.

Example 2: Let's look at the previous example to see how to use Kirchoff's rules.

Rework the entire problem using current sum-rules and three voltage loops.

Kirchoff's first law allows us to sum all the currents at the black junction:

If we knew the currents, then we could just solve the problem. To find the currents, we need to know the voltage drops across each resistor. We use the three loops to show that the voltage across each resistor is equal to the battery voltage. Cool! Each current is then calculated through simple Ohm's Law. And, we get the same answer.

Important points

• The sum of all the currents into a circuit node or junction is zero i.e., add up the currents entering and it must equal the current leaving (Conservation of charge).
• Add up the voltage drops around a loop and you get zero (Conservation of energy).