Chapter 21: RLC Circuits

Chapter 21: RLC Circuits

PHY2054: Chapter 21

1

Voltage and Current in RLC Circuits

?AC

emf source: ¡°driving frequency¡± f

¦Å = ¦Å m sin ¦Øt

?If

circuit contains only R + emf source, current is simple

i=

?If

¦Å

R

= I m sin (¦Øt )

Im =

¦Åm

R

( current amplitude )

L and/or C present, current is not in phase with emf

i = I m sin (¦Øt ? ¦Õ )

?Z,

¦Ø = 2¦Ð f

Im =

¦Åm

Z

¦Õ shown later

PHY2054: Chapter 21

2

AC Source and Resistor Only

?Driving

voltage is ¦Å = ¦Å m sin ¦Øt

i

?Relation

of current and voltage

i =¦Å /R

i = I m sin ¦Øt

? Current

Im =

¦Åm

¦Å ~

R

R

is in phase with voltage (¦Õ = 0)

PHY2054: Chapter 21

3

AC Source and Capacitor Only

q

= ¦Å m sin ¦Øt

?Voltage is vC =

C

?Differentiate to find current

q = C¦Å m sin ¦Øt

i

i = dq / dt = ¦ØCVC cos ¦Øt

?Rewrite

using phase (check this!)

i = ¦ØCVC sin (¦Øt + 90¡ã )

?Relation

¦Å ~

C

of current and voltage

i = I m sin (¦Øt + 90¡ã ) I m =

?¡°Capacitive

? Current

¦Åm

XC

( X C = 1/ ¦ØC )

reactance¡±: X C = 1/ ¦ØC

¡°leads¡± voltage by 90¡ã

PHY2054: Chapter 21

4

AC Source and Inductor Only

?Voltage

is vL = Ldi / dt = ¦Å m sin ¦Øt

?Integrate

di/dt to find current:

i

di / dt = ( ¦Å m / L ) sin ¦Øt

i = ? ( ¦Å m / ¦Ø L ) cos ¦Øt

?Rewrite

using phase (check this!)

i = ( ¦Å m / ¦Ø L ) sin (¦Øt ? 90¡ã )

?Relation

¦Å ~

L

of current and voltage

i = I m sin (¦Øt ? 90¡ã ) I m =

?¡°Inductive

? Current

¦Åm

XL

( X L = ¦ØL)

reactance¡±: X L = ¦Ø L

¡°lags¡± voltage by 90¡ã

PHY2054: Chapter 21

5

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