1. Current & Circuits October 16, 2006
PHY-2049
Current & Circuits
October 16, 2006

2. This is the week that will be
Monday, Wednesday
Introduction to DC circuits
Brief discussion of not so DC circuits.
Friday
7:30 AM Review Session
Quiz
More on DC.

3. Prelude to DC Circuits

4. Which is brighter?
A B A B
Both the same

5. Which is Brighter? A B
Same

6. B
Brighter? A
A is brighter
B is brighter
Both are the same

7. Last week ...
J and E

8. What does the graph tell us??
The figure below gives the electrical potential V(x) along a copper wire carrying a uniform current, from a point at higher potential (x=0m) to a point at a lower potential (x=3m). The wire has a radius of 2.45 mm. What is the current in the wire?
What does the graph tell us??
copper
12 volts volts
*The length of the wire is 3 meters.
*The potential difference across the
wire is 12 m volts.
*The wire is uniform.
Let’s get rid of the mm radius and
convert it to area in square meters:
A=pr2 = x x 10-6 m2 or
A=1.9 x m 2
Material is Copper so resistivity is (from table) = 1.69 x 10-8 ohm meters

9. We have all we need….

10. Let’s add resistors …….

11. SERIES Resistors
Series Combinations
R R2 i
V V2 V

12. Parallel Combination??
R1, I1
R2, I2 V

13. What’s This???
In Fig , find the equivalent resistance between points (a) F and H and [2.5]  (b) F and G. [3.13]   ?

14. (a) Find the equivalent resistance between points a and b in Figure P28.6. (b) A potential difference of 34.0 V is applied between points a and b. Calculate the current in each resistor.

15. Power Source in a Circuit
The ideal battery does work on charges moving them (inside) from a lower potential to one that is V higher.

16. A REAL Power Source is NOT an ideal batteryV
Internal Resistance
By the way …. this is called a circuit!
E or Emf is an idealized device that does an amount of work E to move a unit charge from one side to another.

17. A Physical (Real) Battery
Internal Resistance

18. Which is brighter?

20. Back to Potential Change in potential as one circuits
Represents a charge in space
Change in potential as one circuits
this complete circuit is ZERO!

21. Consider a “circuit”.
This trip around the circuit is the same as a path through space.
THE CHANGE IN POTENTIAL FROM “a” AROUND THE CIRCUIT AND BACK TO “a” is ZERO!!

22. To remember
In a real circuit, we can neglect the resistance of the wires compared to the resistors.
We can therefore consider a wire in a circuit to be an equipotential – the change in potential over its length is slight compared to that in a resistor
A resistor allows current to flow from a high potential to a lower potential.
The energy needed to do this is supplied by the battery.

23. NEW LAWS PASSED BY THIS SESSION OF THE FLORIDUH LEGISLATURE.
LOOP EQUATION
The sum of the voltage drops (or rises) as one completely travels through a circuit loop is zero.
Sometimes known as Kirchoff’s loop equation.
NODE EQUATION
The sum of the currents entering (or leaving) a node in a circuit is ZERO

24. TWO resistors again i
R R2
V V2 V

25. A single “real” resistor can be modeled as follows:V
position
ADD ENOUGH RESISTORS, MAKING THEM SMALLER
AND YOU MODEL A CONTINUOUS VOLTAGE DROP.

26. If the potential rises … well it is a rise.
We start at a point in the circuit and travel around until we get back to where we started.
If the potential rises … well it is a rise.
If it falls it is a fall OR a negative rise.
We can traverse the circuit adding each rise or drop in potential.
The sum of all the rises around the loop is zero. A drop is a negative rise.
The sum of all the drops around a circuit is zero. A rise is a negative drop.
Your choice … rises or drops. But you must remain consistent.

27. Take a trip around this circuit.
Consider voltage DROPS:
-E +ir +iR = 0 or
E=ir + iR
rise

28. Circuit Reduction
i=E/Req

29. Multiple Batteries
Watch the DIRECTION !!

30. Reduction
Computes i

31. Another Reduction Example
PARALLEL

32. NOTICE ASSUMED DIRECTION OF Currents
Voltage Drops:
-E1 –i1R1 + i2R2 + E2 +i1R1 = 0
From “a”
-i3R1 + E2 – E2 –i2R2 =0
NODE
i3 +i2 = i1

33. In the figure, all the resistors have a resistance of 4
In the figure, all the resistors have a resistance of 4.0 W and all the (ideal)
batteries have an emf of 4.0 V. What is the current through resistor R?

34. Resistors and Capacitors in the same circuit??
The Unthinkable ….
Resistors and Capacitors in the same circuit??
Is this cruel or what??

35. RC Circuit How Fast ? Initially, no current through the circuit
Close switch at (a) and current begins to flow until the capacitor is fully charged.
If capacitor is charged and switch is switched to (b) discharge will follow.
How Fast ?

36. What do you think will Close the Switch happen when we close the
swutch?
Close the Switch
I need to use E for E
Note RC = (Volts/Amp)(Coul/Volt)
= Coul/(Coul/sec) = (1/sec)

37. Really Close the Switch
I need to use E for E
Note RC = (Volts/Amp)(Coul/Volt)
= Coul/(Coul/sec) = (1/sec)

38. This is a differential equation.
To solve we need what is called a particular solution as well as a general solution.
We often do this by creative “guessing” and then matching the guess to reality.
You may or may not have studied this topic … but you WILL!

39. Math !

40. Time Constant

41. Result q=CE(1-e-t/RC)

42. q=CE(1-e-t/RC) and i=(CE/RC) e-t/RC

43. Discharging a Capacitor
qinitial=CE BIG SURPRISE! (Q=CV) i
iR+q/C=0

44. Looking at the graph, we see that the
In Fig. (a), a R = 21, Ohm a resistor is connected to a battery. Figure (b) shows the increase
of thermal energy Eth in the resistor as a function of time t.
What is the electric potential across the battery? (60)
If the resistance is doubled, what is the POWER dissipated by the circuit? (39)
Did you put your name on your paper? (1)
Looking at the graph, we see that the
resistor dissipates 0.5 mJ in one second.
Therefore, the POWER =i2R=0.5 mW

45. If the resistance is doubled what is the power dissipated by the circuit?