1. Thursday(02/18): Intro. to Ch.28, DC Circuits with Resistors in Series

and Parallel. HW: Read and Study pages 858-69, then solve problems 2,

4, 5, 6, 8, and 15 on pages 885-6.

2. Friday(02/19): Kirchoff's Loop and Point Rules. HW: Study pages

869-73, and Solve problems 20, 21, 24, and 26 on pages 887-8.

3. Monday(02/22): LAB on Series Circuits. HW: Process all Lab Data.

Lab Report is due on Wednesday.

4. Tuesday(02/23): RC Circuits (charging and discharging). HW: Read and

Study pages 873-78, then solve problems 31, 32, 34, and 39 on pages 888-9.

5. Wednesday(02/24): Electrical meters, Household Wiring, and Safety.

HW: Read and Study pages 879-83, then solve problems 41, 48, and 49 on

pages 889-90.

6. Thursday(02/25): Review for Ch.28. HW: Complete Review Handout.

7. Friday(02/26): TEST on Ch.28 - DC Circuits. HW: Go to website

and study notes for Ch.29 - Magnetic Fields.

Website Notes on Ch.28 - DC Circuits.

1. The source of electric energy that causes charges to move in electric

circuits is the emf, E. Historically such energy sources were called

electromotive force, however, it is not a "force" but a potential energy per

unit charge, or a voltage.

2. A good example of such a source of electric energy is a battery. When a

battery is placed in a circuit loop with other circuit elements, such as

capacitors or resistors, a DC current flows.

3. The internal chemistry of the battery provides some internal voltage, or

emf, for the battery. The actual terminal voltage of the battery will be

somewhat less due to the voltage drop over the "internal resistance."

4. The expression describing terminal voltage is: V = E - Ir . Here V is the

terminal voltage (measured between the two terminals), E is the true emf

of the battery, I is the current being drawn from the battery, and r is the

battery's internal resistance.

5. We find that: P = Vq/t = VI. For a resistor, this expression can be

rewritten as: P = (IR)I = I²R .

6. Consider a single-loop circuit, one with a single path for current. If we

keep track of the voltage around the loop, and remember that voltage (or

potential, or electric potential) is potential energy per unit charge, we note

that the sum of the potential changes (or potential "drops") around the loop

must be zero.

7. We can summarize Kirchhoff's Loop Rule as: The sum of the potential

changes around a closed path is zero. Σε - ΣIr = 0 . This rule can be for a

simple loop, or for any closed loop in a more complex circuit, say one that

has two or three loops. 

8. We can summarize Kirchhoff's Point Rule as: The algebraic sum of the

currents that enter a junction is zero. Σ I = 0. This rule along with the Loop

Rule will enable us to analyze various electric circuits.

9. For resistors in series, use simple addition: R_EQ = R₁ + R₂ + … + R_n.

10 For resistors in parallel, reciprocals: 1/R_EQ = 1/R₁ + 1/R₂ + … + 1/R_n.

11. RC circuits are circuits that contain both resistors and capacitors. In a DC

circuit (or, steady-state circuit, or constant current circuit), a capacitor acts

like an open switch. Its steady-state voltage will be V = Q/C and will be

equal to the voltage of the battery. However, when the switch is first closed

for the circuit, charge must flow until the capacitor is charged. This is called

a transient current.

12. Consider a simple loop circuit with a battery with terminal voltage,

E = V_battery, a resistor R, a capacitor C, and a switch. Just before the switch

is closed the current is zero. Just after it is closed a current flows and the

capacitor starts to charge. Its voltage will be given by V = q/C. By the time

q grows to Q until Q/C = E , the current will be zero.

13. Let us write Kirchhoff's Loop Rule for the circuit: E - IR - q/C = 0 . Note

that the current I can be written as I = dq/dt. The expression then becomes:

E - (dq/dt)R - q/C = 0 .

14. The solution to this equation is: q(t) = (CE)(1 - e^(-t/RC)) . Note that

after a long time e^(-t/RC) becomes equal to 0, and the charge is constant.

If we take the derivative of q(t) with respect to t, we get the expression:

I = dq/dt = (E/R)e^(-t/RC) .

15. We see that after a long time, the current is zero. The quantity RC is

16. If we start with a charged capacitor, and have only a resistor and an open

switch in the circuit, we can then discharge the capacitor by closing the switch.

The Kirchhoff's Loop Rule equation becomes:  - IR - q/C = 0 . Again, using

I = dq/dt, and substituting we now have : E - (dq/dt)R - q/C = 0 .

The solution is: q(t) = Q_oe^(-t/RC) . Here Q_o = CE. Again, using I = dq/dt, we

have: I(t) = (Q_o/RC)e^(-t/RC) = (E/R)e^(-t/RC) . After a time interval equal

to one time constant τ has passed, the charge is 63.2% of the maximum

value at CE.

17. Both the charge and the current become zero after a time as the capacitor

is discharged. For a measure of the time we use the time constant τ = RC.

When t = RC, we get the value that e^(-t/RC) = e^-1 = 0.37, or the charge on

the capacitor is down to just over one-third of the original value.

18. A decrease of potential energy can occur by various means. For example,

heat lost in a circuit due to some electrical resistance could be one source of

energy drop.

19. And still, we need these steps to solve any problem in Physics:

(i) read the problem and identify the given variables

(ii) determine what you are asked to solve for

(iii) find the correct equation to use

(iv) use Algebra, Trigonometry, and/or Calculus to isolate the unknown

(v) substitute-in the given information and simplify.

THE AP PHYSICS C ARCHIVES Ch.1: Physics Intro. Ch.2: Linear Motion. Ch.3: Vectors. Ch.4: 2-Dim Motion. Ch.5&6: Newton's Laws. Ch.7&8: Work&Energy. Ch.9: Momentum. Ch.10&11: Rotary Motion. Ch.12: Elasticity. Ch.13: Gravitation. Ch.15: SHM. Mechanics Review. Ch.23: Electric Fields. Ch.24: Gauss's Law. Ch.25: Electric Potential. Ch.26: Capacitance. Ch.27: Current/Resistance. Ch.28: DC Circuits.