Chapter 21: RLC Circuits

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Chapter 21: RLC Circuits - Department of Physics

PHY2054: Chapter 21

PHY2054: Chapter 21

Voltage and Current in RLC Circuits

AC emf source: "driving frequency" f

If circuit contains only R + emf source, current is simple

If L and/or C present, current is

not in phase with emf

Z, shown later

sin mmm iI t I Z sin m t 2f sin current amplitude mmm iI tI R R

PHY2054: Chapter 21

AC Source and Resistor Only

Driving voltage is

Relation of current and voltage

Current is

in phase with voltage (= 0) i R sin mmm iI tI R sin m t /iR

PHY2054: Chapter 21

AC Source and Capacitor Only

Voltage is

Differentiate to find current

Rewrite using phase (check this!)

Relation of current and voltage

"Capacitive reactance":

Current "leads" voltage by 90

sin m qC t i C /cos C idqdt CV t sin Cm qvtC sin 90 C iCV t sin 90 mmm C iI t IX 1/ C XC 1/ C X C

PHY2054: Chapter 21

AC Source and Inductor Only

Voltage is

Integrate di/dt to find current:

Rewrite using phase (check this!)

Relation of current and voltage

"Inductive reactance":

Current "lags" voltage by 90

//sin m di dt L t i L /cos m iLt /sin Lm v Ldi dt t /sin 90 m iLt sin 90 mmm L iI t IX L XL L XL

PHY2054: Chapter 21

General Solution for RLC Circuit

We assume steady state solution of form I m is current amplitude is phase by which current "lags" the driving EMF

Must determine I

m and

Plug in solution: differentiate & integrate sin(

t- sin m iI t cos sin cos sin mmm m I I

LtIRt t tC

Z sin m di qLRi tdt C sin m iI t cosquotesdbs_dbs2.pdfusesText_2

[PDF] Chapter 21: RLC Circuits - Department of Physics