physics 2112 unit 18 - college of dupage · 2020. 4. 1. · electricity & magnetism lecture 18,...

Physics 2112

Unit 18

Today’s Concepts:A) Induction

B) 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

What if you only had the outer set of loops?

Would changing current in that induce anything?

1. Changing current in outer

set of loops

2. Caused changing magnetic

field in inner loops

3. Induced changing current in

inner loops.

Self Inductance


IL B

dt

dIL

dt

LId

dt

d 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 long coil of wire (a solenoid)?

Example 18.1 (Inductance of Solenoid)


Increasing current

What the minus sign means…..


dt

dIL−=

DV < 0VA > VB

A B

Acts like a resistor

IAB DVAB

zrnLB

22

0 =

volumen *2

0=

decreasing current

What the minus sign means…..


dt

dIL−=

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

dIdt

L = −L

emf induced across L tries to keep I constant.

Inductors prevent discontinuous current changes!

It’s like inertia!

What this really means:


Units of inductance are Henrys (H) [Tm2/A]

RL

VBATT

I = 0

Time Constant


R

L=

)1( /teR

VI −−=

R=120WL

12V= VBATT

S

Example 18.2 (Current in Solenoid)


R

L=)1( /te

R

VI −−=

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 = 0

VL = 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:


VL

R

L=

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


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/RI

I

Confusion about question….


C) there is no current at t=0

I mean a little “dt” of time after t=0

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


RL

VBATT

I = V/R

At t >> L/R:

I = 0

VL = 0

VR = 0

R

I = 0

LR

I = VBATT/R

VR = IR

VL = VR

At t = 0:

When steady current is flowing initially:

How to Think about RL Circuits Episode 2:

VL

R

L=

R

L=


R

I

V = IRdIdt

V = L L

+

−

−

+

Why is there Exponential Behavior?

VL

R

L=

R

L=


0=+ IRdt

dIL

whereR

L=

/0

/

0)( tLtR eIeItI −− ==

Prelecture:

RL

I

Lecture:

VL

VBATT

Did we mess up?

No: The resistance is simply twice as big in one case.

R

L=


Quick comment…

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?


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



After switch moved, which case has larger time constant?


R

L

21 =

R

L

32 =

CheckPoint 3A



CheckPoint 3B



Immediately after switch moved, in which case is the voltage across the inductor larger?


Before switch moved: R

VI =

After switch moved:

RR

VVL 21 =

RR

VVL 32 =

CheckPoint 3B



Immediately after switch moved, in which case is the voltage across the inductor larger?


CheckPoint 3C



After switch moved for finite time, in which case is the current through the inductor larger?


Immediately after: 21 II =

After awhile

1/

1t

IeI−

=

2/

2t

IeI−

=

21 >

CheckPoint 3C



After switch moved for finite time, in which case is the current through the inductor larger?

Energy Stored

Unit 18, Slide 27

VIdt

energydPower ==

)(

2

2

1LIEstored =

2

2

1

C

QEstored =

For inductor Recall for capacitor

Energy stored in

the magnetic field

Energy stored in

the electric field

R=100WL

12V= VBATT

S

Example 18.3 (Energy in Solenoid)


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 energy stored in the inductor 0.01sec after the switch is closed?

What is the energy stored in the inductor 2.0 sec after the switch is closed?

2

2

1LIEstored =

A. 0A

B. 4A

C. 6A

D. 12A

E. -4A

120V

The switch has been in the open position for a long

time in the circuit drawn above. What is the total

current out of the battery, Itot, immediately after the

switch is closed? (The inductor is “ideal”.)

Question

A. 0A

B. 4A

C. 6A

D. 12A

E. -4A

120V


time in the circuit drawn above. What is the current

across the resistor, I1, immediately after the switch

is closed? (The inductor is “ideal”.)

Question

A. 0A

B. 4A

C. 6A

D. 12A

E. -4A

120

V


time in the circuit drawn above. What is the current

across the inductor, I2, immediately after the switch

is closed? (The inductor is “ideal”.)

Question

A. 0V

B. 80V

C. 90V

D. 120V

E. 240V

120

V


time in the circuit drawn above. What is the voltage

drop across the inductor immediately after the


Question

A. 0A

B. 4A

C. 6A

D. 12A

E. -4A

120V

The switch has been in the closed position for a

long time in the circuit drawn above. What is the

current across the inductor, I2? (The inductor is

“ideal”.)

Question

A. 0V

B. 80V

C. 90V

D. 120V

E. 240V

120

V



voltage difference across the inductor immediately

after the switch is opened? (The inductor is “ideal”.)

Question

A. 0A

B. 4A

C. 6A

D. 12A

E. -4A

120V



current across the inductor, I2 immediately after the

switch is open? (The inductor is “ideal”.)

Question

A. 6A/sec

B. 80A/sec

C. 90A/sec

D. 120A/sec

E. 240A/sec

120

V



rate change for the current through the inductor

immediately after the switch is opened? (The

inductor is “ideal”.)

Question

A. VA > VB

B. VA = VB

C. VA < VB

120

V


time in the circuit drawn above. Which point has a

higher electrical potential immediately after the


Question

A

B

A. VA > VB

B. VA = VB

C. VA < VB

120

V


long time in the circuit drawn above. Which point

has a higher electrical potential? (The inductor is

“ideal”.)

Question

A

B

A. VA > VB

B. VA = VB

C. VA < VB

120

V


long time in the circuit drawn above. Which point

has a higher electrical potential immediately after

the switch is opened? (The inductor is “ideal”.)

Question

A

B

physics 2112 unit 18 - college of dupage · 2020. 4. 1. · electricity & magnetism lecture 18,...

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