physics 2112 unit 18
Post on 22-Feb-2016
103 Views
Preview:
DESCRIPTION
TRANSCRIPT
Physics 2112Unit 18
Today’s Concepts:A) InductionB) RL Circuits
Electricity & Magnetism Lecture 18, Slide 1
Where we are…..
Unit 17, Slide 2
Just finished introducing magnetism
Will now apply magnetism to AC circuits
Remember Example 17.6 (solenoid)??
Unit 17, Slide 3
1. Changing current in outer
loop
2. Caused changing magnetic
field in inner loop
3. Induced changing current in
inner loop.
What if you only had one loop?
Would changing current in that induce anything?
Self Inductance
Electricity & Magnetism Lecture 18, Slide 4
IL B
dtdIL
dtLId
dtd B
)(
Define:Depends only
on the geometry of
the coils
Voltage drop in a coil
…caused by changes in
the current in that same
coil
L
What is the inductance of a solenoid?
Example 18.1 (Inductance of Solenoid)
Electricity & Magnetism Lecture 18, Slide 5
Two solenoids are made with the same cross sectional area and total number of turns. Inductor B is twice as long as inductor A
Compare the inductance of the two solenoids A) LA 4 LB B) LA 2 LB C) LA LB D) LA (1/2) LB E) LA (1/4) LB
Checkpoint 1
Electricity & Magnetism Lecture 18, Slide 6
zrnLB22
0
Increasing current
What the minus sign means…..
Electricity & Magnetism Lecture 18, Slide 7
dtdIL
DV < 0VA > VB
A A
Acts like a resistor
IAB DVAB
decreasing current
What the minus sign means…..
Electricity & Magnetism Lecture 18, Slide 8
dtdIL
DV > 0VA < VB
A B
Acts like a battery
IAB DVAB
However you try to change the current
through an inductor, the inductor resists that
change.
current I
L
dIdtL L
emf induced across L tries to keep I constant.
Inductors prevent discontinuous current changes!
It’s like inertia!
What this really means:
Electricity & Magnetism Lecture 18, Slide 9
Units of inductance are Henrys (H) [Tm2/A]
RL
VBATT
I 0
Time Constant
Electricity & Magnetism Lecture 18, Slide 10
RL
)1( /teRVI
R=100WL
12V= VBATT
S
Example 18.2 (Current in Solenoid)
Electricity & Magnetism Lecture 18, Slide 11
RL
)1( /teRVI
A solenoid has 6500 loops in a length of 10cm and a radius of 6cm. It is attached to a 120W resistor and a 12V battery.
What is the current through the resistor 0.01sec after the switch is closed?
What is the current through the resistor 2.0 sec after the switch is closed?
Would the current have been at 0.01sec if the inductor had an internal resistance of 20W?
RL
At t = 0:I 0VL VBATT
VR 0(L is like a giant resistor)
VBATT
I 0
At t >> L/R:VL 0 VR VBATT
I VBATT/R(L is like a short circuit)
R
I = V/R
L
VBATT
When no current is flowing initially:
How to think about RL circuits:
Electricity & Magnetism Lecture 18, Slide 12
VL
RL
I
What is the current I through the vertical resistor immediately after the switch is closed? (+ is in the direction of the arrow)
A) I V/R B) I V/2R C) I 0 D) I V/2R E) I V/R
In the circuit, the switch has been open for a long time, and the current is zero everywhere.
At time t 0 the switch is closed.
I
I
CheckPoint 2A
Electricity & Magnetism Lecture 18, Slide 13
What is the current I through the vertical resistor immediately after the switch is opened?
(+ is in the direction of the arrow)
A) I V/R B) I V/2R C) I 0 D) I V/2R E) I V/R
After a long time, the switch is opened, abruptly disconnecting the battery from the circuit.
CheckPoint 2B
Electricity & Magnetism Lecture 18, Slide 14
RL
VBATT
I V/R
At t >> L/R:I 0VL 0VR 0
R
I = 0
LR
I VBATT/RVR IR VL VR
At t 0:
When steady current is flowing initially:
How to Think about RL Circuits Episode 2:
VL
RL
RL
Electricity & Magnetism Lecture 18, Slide 15
R
I
V IRdIdtV L L
+
+
Why is there Exponential Behavior?
VL
RL
RL
Electricity & Magnetism Lecture 18, Slide 16
0+ IRdtdIL
whereRL
/0
/0)( tLtR eIeItI
Inside your i-clicker
” Can you have capacitors and inductors in the same circuit?“why inductors are important as opposed to capacitors. why use one instead of the other?”
What are Inductors and Capacitors Good For?
Electricity & Magnetism Lecture 18, Slide 17
Prelecture:
RL
I
Lecture:
VLVBATT
Did we mess up?
No: The resistance is simply twice as big in one case.
RL
Electricity & Magnetism Lecture 18, Slide 18
Quick comment…
After long time at 0, moved to 1 After long time at 0, moved to 2
After switch moved, which case has larger time constant?
A) Case 1B) Case 2C) The same
CheckPoint 3A
Electricity & Magnetism Lecture 18, Slide 19
A) Case 1B) Case 2C) The same
CheckPoint 3B
Electricity & Magnetism Lecture 18, Slide 20
After long time at 0, moved to 1 After long time at 0, moved to 2
Immediately after switch moved, in which case is the voltage across the inductor larger?
A) Case 1B) Case 2C) The same
CheckPoint 3C
Electricity & Magnetism Lecture 18, Slide 21
After long time at 0, moved to 1 After long time at 0, moved to 2
After switch moved for finite time, in which case is the current through the inductor larger?
Conceptual AnalysisOnce switch is closed, currents will flow through this 2-loop circuit. KVR and KCR can be used to determine currents as a function of time.
Strategic AnalysisDetermine currents immediately after switch is closed.Determine voltage across inductor immediately after switch is closed.Determine dIL/dt immediately after switch is closed.
R1
LV
R2
R3
Example 18.3 (3R and L circuit)
The switch in the circuit shown has been open for a long time. At t 0, the switch is closed.
Electricity & Magnetism Lecture 18, Slide 22
What is dIL/dt, the time rate of change of the current through the inductor immediately after switch is closed?
top related