Fundamental of Circuits.
Sec 28.1-28.8
This week we read Chap 28 except for the last section on RC circuits which we
keep for next week. We will start by analyzing fundamental circuits this week
with only resistors and batteries (and light bulbs which act like resistors to a good
approximation).
Our first task when analyzing circuits is to write a "circuit diagram". This is a simplified drawing
of a real circuits with multiple wires. It does require practice to go from an
actual real circuit to a circuit diagram. Here are the various circuits
symbols that we will use.
Notice how the lightbulb image has 2 wires inside connected to two different outside
metal conductors. As you should have discovered in your lab 3, a lightbulb has
two ends like the other circuit elements we will learn in this class.
Section 28.2 is the crucial section from a physics point of view. The master
equations for circuits are Kirchhoff's laws Eq 28.1 and Eq 28.2. Tactics box
28.1 is super important in explaining how to use those laws.
The sign conventions for the change in potential across a battery and resistor
are crucial to learn. The voltage difference across a resistor is negative in the direction of the current. The voltage difference across a battery is positive if the battery is aligned - then + along the current, the voltage will be negative if the battery is in the opposite direction.
Section 28.3 define the notion of power as the rate of thermal energy
dissipated in a resistor. The general formula is
P_R=I\Delta V_R
which just comes from taking the
derivative with respect to time of the potential energy U=qV where dq/dt
becomes the current.
There are two reformulations of this equation using Ohm's law and both are
important in this context (see the check your understanding for good examples
of where one formula is needed compared to the other).
P_R = I^2 R=\frac{(\Delta V_R)^2}{R}
We then analyze resistor in series, resistors in parallels and real batteries
with internal resistance.
This chapter explains how a voltmeter (such as the IOLab) is used in parallel
and how it needs to have a high resistance in order not to disturb the
circuit. A ammeter needs to be in series in the circuit and needs to have a
small resistance. The compass is our ammeter (and it has a very small
resistance!).
Section 27.7 introduces the case of multi-loop circuits where one needs to be
more methodical. Look carefully at problem solving strategy 28.1
and the two
worked out examples 28.9, 28.10. The idea is to use Kirchhoff's two laws (Eq
28.1 and 28.2) for the whole circuit. Kirchhoff's loop law applies to any loop
in the circuits. You will get multiple equations (one for each loop) allowing
you to solve for multiple unknowns.
We keep section 28.9 for next week while section 28.8 explains the concept of
grounding.
Here is a demonstration of a parallel vs series circuits.
Doing the worked out example problems.
For the more complicated examples, do not just read the solutions in the book
right away. I recommend the following procedure.
- First, you read the example question ONLY.
-
You take a piece of paper and try to solve it, without looking at the
solution.
-
You may need to study the material, read the text before the example. Pay
particular attention to problem solving strategies or tactic boxes.
-
You may need to struggle, abandon one way and try another. This is good.
This is learning.
-
If you get the answer, compare just the solutions to the one in the book. If
its the same, great, now look at what the author did. If its not the same,
look back at your process first and try to find where you could have gone
wrong.
-
If after 2 attempts (say 1/2 hour at least), it does not work look at the
solution provided by the author. You will need to try a similar problem
again later to make sure you can do it without help.
All the worked examples in this chapter are worth doing with many of them being
very simple (just one equation). Example 28.6 shows you why car batteries are
dangerous.