30. Inductance.

1-2. Self & Mutual Inductance Inductance:

B Bd d diN Ndt di dt

E=

unit : H (henry)

Mutual Inductance

22 2

2 12

1

121

B

B

dN

dtd di

Ndi dt

diM

dt

E =

Self Inductance and inductor (or choke)

Bd diL

dt dt

E=

BdL N

di

Potential change

a b

diV V L

dt

3. Magnetic Field Energy

Energy stored in an inductor

2

0

1

2

IU L idi LI

diP Vi Li

dt

4. The R-L Circuit

0di

iR Ldt

E

di Ri

dt L L

E

dq q

dt RC R

E

0q

iRC

E

/( ) (1 )t RCq t C e E

R-C circuit

( / )1 R L ti eR

E

Current Growth

Current graph

Power in Current growth :

2 diP i R Li

dt p

Current Decay

0di

iR Ldt

0di R

idt L

( / )0

R L ti I e

20di

i R Lidt

Power

Problem 30.64) Find the reading in each ammeter and voltmeter at the following times

a) just after switch S is closed

b) after S has been closed a very long time.

Problem 30-65) Switch S is closed at t=0 with no charge initially on the capacitor.

a) Find the reading of each ammeter and each voltmeter just after S is closed.

b) Find the reading of each ammeter and each voltmeter after a long time has elapsed.

c) Find the maximum charge on the capacitor.

5. L-C Circuit Oscillating L-C circuit

Applet http://www.walter-fendt.de/ph11e/osccirc.htm http://physics.bu.edu/~duffy/semester2/c19_LC.html

Electrical oscillation

0di q

Ldt C

2

2

10

d qq

dt LC

2

20

d x kx

dt m

( ) cos( )q t Q t

Simple Harmonic oscillation

1

LC

Comparison with mass-spring system

Example 30.9) 300 V was charged to a 25F capacitor. Then, disconnected from power, connected to 10 mH inductor. Find

a) frequency and period

b) charge and current at t=1.2 ms.

Example 30.10) Find the magnetic and electric energy of the circuit of Example 30.9).

a) t=0, b) t=1.2 ms

Problem 30.34) An L-C circuit. When i=Imax , find

a) Maximum energy stored in the capacitor

b) How often you will have that energy?

6. L-R-C circuit

L-R-C circuit

Underdamped oscillation solution

0di q

iR Ldt C

2

2

10

d q R dqq

dt L dt LC

Underdamped oscillation solution

( / 2 )( ) cos( )R L tq t Ae t

21

2

R

LC L

Example) An L-R-C circuit.

a) When R=0, what is the angular frequency?

b) what value R must be to give n% decrease in angular frequency compared to the result a)