Download Circuit Elements: capacitor, resistor, and Ohm`s law

Phy2005
Applied Physics II
Spring 2017
Announcements:
• Solutions to Ch. 20 posted on HW page
• Answers to chapter 21 problems posted on HW page
• Practice Exam 1 (S16) posted on tests page
• Exam 1 Wed. Feb. 8 in class. Covers chs. 19-21;
• Test: bring ID, calculator; 1 handwritten formula sheet ok
• PH gone Friday, Feb. 3; lecture by Dr. Saurabh Maiti
Science news page
Aurora Borealis
http://www.aurorahunter.com/how-the-aurora-borealis-form.php
Last time:
microscopic picture of conduction
Ions
E
. Average speed of electrons in wire: about c/10:
2. Drift velocity of electrons: very slow, less than 1
cm/sec. This velocity corresponds to the current we
calculate.
3. Velocity of information, energy flow. Close to c.
Power = work done against electric forces/time
P=IV for circuit element with current I
through it and voltage V across it
For resistor, V=IR, so also P=V2/R, I2R
Caveat: remember what quantity is held fixed in a given
circuit if something changes!!!
Today: T-dependence of resistance, Kirchoff’s laws
ACADEMIC HONESTY
Each student is expected to hold himself/herself to a high standard
of academic honesty. Under the UF academic honesty policy.
Violations of this policy will be dealt with severely. There will be
no warnings or exceptions.
5W
A 12V battery is connected from a to b.
Find the current that flows in the 3W
resistor.
4W
3W
a
b
1.
2.
3.
4.
5.
5.2 Amp
5.2 V
2.3 Amp
2.3 V
4 Amp
Ex Two different shape of wires are made out of copper.
The first one has a 1 mm radius and 1 m long. The second wire
has 0.5 mm radius and 25 cm long. Calculate their resistances.
rcopper = 1.7 x 10-8 Wm
R = rL/A
R1 = R2 = 5.4 x 10-3 W
Specifications: 40 W/120 V
P = IV = V2/R = 40 (W)
R = 1202/40 = 367 (W)
But if you take out and measure resistance
of the bulb with an ohmmeter, find Rmeasured ≈ 26 W
Why are they so different?
metals
r
Filament at room T:
25 degrees Celsius
26 W
Operating bulb:
2550 degrees Celsius
367 W
insulators
Temperature
However, insulators have the opposite tendency.
The higher temperature, the lower R.
r depends on temperature!!!
In 1913, a ground breaking observation was made
in a laboratory in Leiden (Netherlands).
Van der Waals
Kammerlingh Onnes
Superconductivity!
Kirchoff’s Laws
(1) Node rule, current law,..
I2
I1 = I2 + I3
I1
I3
=
+
V1=IR1
(2) Loop rule, V-law,..
D
B
C
R1
V
A
V2=IR2
R2
E
F
V1
V
V2
A
B
C
D
E
F
A
IR1
IR2
R1
R2
V
R3
I
V
V – IR1 – IR2 – IR3 = 0
V = I (R1 + R2 + R3)
= I Req
IR3
I1
I
I2
R1
R2
R3
I3
4 unknowns
Need 4 independent eqs.
V
(1) I = I1 + I2 + I3
(2) V – I1R1 = 0
V/R1 = I1
(3) V – I2R2 = 0
V/R2 = I2
(4) V – I3R3 = 0
V/R3 = I3
V (1/R1+1/R2+1/R3) = I
1/Req
V = IReq
How do we measure I or potential drop in a circuit?
Measuring instruments should not change the values!!
A
V
Ammeter
A
Should have ideally zero internal resistance.
Voltmeter
V
Should have ideally infinite internal resistance.
RECIPE
(1) Indicate currents going through each circuit elements:
* Realize that the same I flows through elements up to
the junction points.
* Make your best educated guess on the directions of I’s.
(2) The currents are your unknowns.
* You have to set up the same number of indep. Eqs.
* At least one of them come from the I-law and the rest of
them are from the V-law
(3) Set up the appropriate loops and apply V-law for each
loop. The direction of each loop can be either CW or CCW.
* If the loop runs from (+) to (-) of a battery, the battery
contributes (+) voltage (vice versa).
* If the loop runs in the same direction as that of your
current, the resistor contributes (-) voltage calculated
from Ohm’s Law (vice versa).
* Add all the contributions from the elements (R’s and
batteries) in the loop will be set to “0”. 1 equation.
++ After all, if you get (-) current value, that simply means
the current flows in the direction opposite to your guess.
I3
I1, I2, and I3
3 unknowns
6V
5
I2
3
I1
8 V
I1 = I 2 + I 3
6 – 5*I2 – 8 = 0
2 + 5*I2 = 0
6 – 3*I3 = 0
I3 = 2 A
I1 = 1.6 A
I2 = - 0.4 A
This means that
Your guess on the
direction of I2 was wrong
and actual current flows
opposite direction.
ACADEMIC HONESTY
Each student is expected to hold himself/herself to a high standard
of academic honesty. Under the UF academic honesty policy.
Violations of this policy will be dealt with severely. There will be
no warnings or exceptions.
24 V
1.
2.
3.
4.
5.
Both go out
the intensity of light bulb A increases
the intensity of light bulb B increases
the intensity of light bulb A decreases
nothing changes
Example 21.3
40
3 V
50
4 V
I1
10
5 V
I2
20
I3
30
I2 = I1 + I3
4 – 40I1 – 3 – 10I1 – 20I2 = 0
4 – 50I3 – 5 – 30I3 – 20I2 = 0
1 – 50I1 – 20I2 = 0
-1 – 80I3 – 20I2 = 0
Does Ohm’s law say this?
• Ohm: A liquid measure formerly used in Germany, varying
locally between 30 and 36 gallons.
• With the same potential drop (voltage) applied, the larger
current flows through the smaller resistance.
• With the same current flowing, larger potential drop develops
across the larger resistance.
• If the resistance is infinite, no current flows regardless of
potential (voltage) difference across the resistor.
• When there is no potential difference across an element, no
current flows through regardless of the resistance.