Chapter 21: RLC Circuits

Chapter 21: RLC Circuits

PHY2054: Chapter 21

1

Voltage and Current in RLC Circuits

?AC emf source: "driving frequency" f

= m sint

= 2 f

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

i

=

R

=

Im

sin (t )

Im

=

m

R

(current amplitude)

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

i = Im sin (t - )

Im

=

m

Z

?Z, shown later

PHY2054: Chapter 21

2

AC Source and Resistor Only

?Driving voltage is = m sint

?Relation of current and voltage

i = /R

i = Im sint

Im

=

m

R

i

~

R

Current is in phase with voltage ( = 0)

PHY2054: Chapter 21

3

AC Source and Capacitor Only

?Voltage is

vC

=

q C

=

m

sin t

?Differentiate to find current

q = Cm sint

i

i = dq / dt = CVC cost

~

C

?Rewrite using phase (check this!)

i = CVC sin (t + 90?)

?Relation of current and voltage

i = Im sin (t + 90?)

Im

=

m

XC

( XC = 1/C)

?"Capacitive reactance": XC = 1/C

Current "leads" voltage by 90?

PHY2054: Chapter 21

4

AC Source and Inductor Only

?Voltage is vL = Ldi / dt = m sint

?Integrate di/dt to find current:

di / dt = (m / L)sint i = -(m /L)cost

?Rewrite using phase (check this!)

i = (m /L)sin (t - 90?)

i

~

L

?Relation of current and voltage

i = Im sin (t - 90?)

Im

=

m

XL

(XL =L)

?"Inductive reactance": X L = L

Current "lags" voltage by 90?

PHY2054: Chapter 21

5

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