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Lecture 07. Current & Circuits October 11, 2005. Dis week …. Monday – finish resistance and current and begin electric circuit. There is a new WA on board. Friday – Quiz on Monday-Wednesday’s material NEXT FRIDAY – Examination #2 Studying is a good idea!. Last time. J and E. - PowerPoint PPT Presentation
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Lecture 07
Current & CircuitsOctober 11, 2005
Dis week …
Monday – finish resistance and current and begin electric circuit.
There is a new WA on board. Friday – Quiz on Monday-
Wednesday’s material NEXT FRIDAY – Examination #2
Studying is a good idea!
J and E
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Consider a wire
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Micro-View “Resistivity”
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depends on the material and is the mean time between collisions
ease of motion – mobilityresistance to motion - scattering
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Power
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ELECTRONs
Battery supplies energy to the resistor which, in turn, dissipates it in the form of heat.
Work done on charge Q = Q x V
RiiRiiVVt
Q
t
QVP
PPOWERtimeWork
2
/
REMEMBER: P=iV and P=i2R
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?
copper
12 volts 0 volts
What does the graph tell us??
*The length of the wire is 3 meters.*The potential difference across the
wire is 12 volts.*The wire is uniform.
Let’s get rid of the mm radius and convert it to area in square meters:A=r2 = 3.14159 x 2.452 x 10-6 m2
orA=1.9 x 10-5 m 2
Material is Copper so resistivity is (from table) = 1.69 x 10-8 ohm meters
We have all we need….
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What’s This???
In Fig. 28-39, find the equivalent resistance between points (a) F and H and [2.5] (b) F and G. [3.13]
Moving on …..
Fun and Frolic With Electric Circuits
Power Source in a Circuit
V
The ideal battery does work on charges moving them (inside) from a lower potential to one that is V higher.
A REAL Power Sourceis NOT an ideal battery
V
E or Emf is an idealized device that does an amount of work E to move a unit charge from one side to another.
By the way …. this is called a circuit!
Internal Resistance
A Physical Battery
Internal Resistance Rr
Emfi
Back to Potential
Represents a charge in space
Change in potential as one circuitsthis complete circuit is ZERO!
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!!
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.
VqW
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
TWO resistors againi
R1 R2
V1 V2
V
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RR
Resistors SERIESfor General
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A single “real” resistor can be modeledas follows:
R
a b
V
position
ADD ENOUGH RESISTORS, MAKING THEM SMALLERAND YOU MODEL A CONTINUOUS VOLTAGE DROP.
Take a trip around this circuit.
Consider voltage DROPS:
-E +ir +iR = 0or
E=ir + iRrise
Circuit Reduction
i=E/Req
Multiple Batteries
Reduction
Computes i
Another Reduction Example
PARALLEL
1212
1
600
50
30
1
20
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NOTICE ASSUMED DIRECTION OF TRAVEL
Voltage Drops:-E1 –i1R1 + i2R2 + E2 +i1R1 = 0
From “a”
-i3R1 + E2 – E2 –i2R2 =0 NODEI3 +i2 = i1
In the figure, all the resistors have a resistance of 4.0 and all the (ideal) batteries have an emf of 4.0 V. What is the current through resistor R?
The Unthinkable ….
RC Circuit
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.
Close the Switch
I need to use E for E
Note RC = (Volts/Amp)(Coul/Volt) = Coul/(Coul/sec) = (1/sec)
Really Close the Switch
I need to use E for E
R
E
RC
q
dt
dq
or
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q
dt
dqR
C
qiRE
dt
dqi since
0
Equation Loop
Note RC = (Volts/Amp)(Coul/Volt) = Coul/(Coul/sec) = (1/sec)
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!
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RC
Result q=CE(1-e-t/RC)
q=CE(1-e-t/RC) and i=(CE/RC) e-t/RC
RCteR
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Discharging a Capacitor
qinitial=CE BIG SURPRISE! (Q=CV)i
iR+q/C=0
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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.
(a)What is the electric potential across the battery? (60)(b) If the resistance is doubled, what is the POWER dissipated by the circuit? (39)(c) Did you put your name on your paper? (1)
Looking at the graph, we see that theresistor dissipates 0.5 mJ in one second.
Therefore, the POWER =i2R=0.5 mW
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If the resistance is doubled what is the power dissipated by the circuit?
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