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?