1. PHY-2049
Chapter 27
Circuits

2. A closed circuit
Hot, Hot Hot

3. Power in DC Circuit

4. #24 chapter 26: 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 uvolts 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

5. We have all what we need….

6. Let’s add resistors …….

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

8. The rod in the figure is made of two materials
The rod in the figure is made of two materials. The figure is not drawn to scale. Each conductor has a square cross section 3.00 mm on a side. The first material has a resistivity of 4.00 × 10–3 Ω · m and is 25.0 cm long, while the second material has a resistivity of 6.00 × 10–3 Ω · m and is 40.0 cm long. What is the resistance between the ends of the rod?

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

10. What’s This???
#26 chapter 27:In Figure below, find the equivalent resistance between points (a) F and H and [2.5]  (b) F and G. [3.13]   ?

11. 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.

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

13. A Physical (Real) Battery
Internal Resistance

14. Back to which is brighter?

16. 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!

17. 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!!

18. 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.

19. LOOP EQUATION NODE 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

20. Take a trip around this circuit.
Consider voltage DROPS:
ε-ir -iR = 0 or
ε=ir + iR

21. Circuit Reduction
i=ε/Req

22. Multiple Batteries
Watch the DIRECTION !!

23. Reduction
Computes i

24. Another Reduction Example
PARALLEL

25. START by assuming a DIRECTION for each Current
Let’s write the equations.

26. Resistors and Capacitors in the same circuit??

27. 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 ?

28. Really Close the Switch

29. 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.

30. Result q=Cε(1-e-t/RC)

31. q=Cε(1-e-t/RC) and i=(Cε/RC) e-t/RC

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