Presented by Byoung-Kuk Lee, Ph. D., Senior IEEE

Presented by Byoung-Kuk Lee, Ph. D., Senior IEEE

Energy Mechatronics Lab.

College of Information and Communication Eng.

Sungkyunkwan University Tel: +82-31-299-4581 Fax: +82-31-299-4612 http://seml.skku.ac.kr EML: [email protected]

Inductance, Capacitance, and Mutual Inductance (Part I)

6.1 The Inductor

• The inductance is a linear circuit parameter that relates the voltage induced by a time-varying magnetic field to the current producing the field.

where v is measured in volts, L in henrys, i in amperes, and t in seconds.

1) If the current is constant (di/dt = 0), the voltage across the ideal inductor is zero. (a short circuit)

2) Current can not change instantaneously in an inductor.

dt

L di

v 

Inductance, Capacitance, and Mutual Inductance (Part I)

The Inductor i-v Equation

 ^



t

vd i t

t L i

0

) 1 (

)

( 

dt L di v 

• Current in an inductor in terms of the voltage across the inductor

Inductance, Capacitance, and Mutual Inductance (Part I)

Power and Energy in the Inductor

 

 



 









vd i t v L

dt Li di vi

p

0

) 1 (



dt Li di dt

p  dw 

2 1 Li w 

• Power in an inductor

• Energy in an inductor

Inductance, Capacitance, and Mutual Inductance (Part I)

Ex. 6.3 (a)–(e)

Inductance, Capacitance, and Mutual Inductance (Part I)

Ex. 6.3 (f)–(g)

Inductance, Capacitance, and Mutual Inductance (Part I)

6.2 The Capacitor

1) If the voltage is constant (dv/dt = 0), the current across the ideal capacitor is zero. (an open circuit)

2) Voltage can not change instantaneously in a capacitor.

displacement current

• The capacitance is a linear circuit parameter that relates the current induced by a time-varying electric field to the voltage producing the field.

where i is measured in amperes, C in farads, v in volts, and t in seconds.

dt

C dv

i 

Inductance, Capacitance, and Mutual Inductance (Part I)

i-v Equation, Power, and Energy of Capacitors

 ^



t

id v t

t C v

0

) 1 (

)

( 

dt C dv i 

 

 



 





 

id v t

i C dt

Cv dv vi

p

0

) 1 (



2

2

1 Cv w 

• Power in a capacitor

• Voltage in a capacitor in terms of the current across the capacitor

• Energy in a capacitor

Inductance, Capacitance, and Mutual Inductance (Part I)

Ex. 6.4

Inductance, Capacitance, and Mutual Inductance (Part I)

Ex. 6.5

Inductance, Capacitance, and Mutual Inductance (Part I)

6.3 Series-Parallel Combinations of Inductance

n

eq

L L L L

L 





 ... 

• Combining inductors in series

Inductance, Capacitance, and Mutual Inductance (Part I)

Series-Parallel Combinations of Inductance

n

eq

L L L

L

... 1 1

1 1

2 1









) ( ...

) ( )

( )

( t

i

t

i

t

i t

i    

• Combining inductors in parallel

Inductance, Capacitance, and Mutual Inductance (Part I)

Series-Parallel Combinations of Capacitance

• Combining capacitors in series

Inductance, Capacitance, and Mutual Inductance (Part I)

Series-Parallel Combinations of Capacitance

n

eq

C C C

C 



 ... 

• Combining capacitors in parallel

Inductance, Capacitance, and Mutual Inductance (Part I)

Series-Parallel Combinations of Inductance

AP. 6.4

Inductance, Capacitance, and Mutual Inductance (Part I)

Series-Parallel Combinations of Capacitance

AP. 6.5

Inductance, Capacitance, and Mutual Inductance (Part I)

Series-Parallel Combinations of Inductance

P. 6.21