PHYS-222 Worksheet 12 for Section 25 & 36
TA: Yang Li, leeyoung@iastate.edu, November 5, 2012
Problem 12: L-R-C series circuit revisit
A capacitor discharges throught a L-R-C series circuit. At beginning, it has 1mC charge. Figure (b) shows
the charge q(t) as a function of time. If given the resistor is 1Ω and the discharging formula for L-R-C series
circuit:
!
r
1
R2
−(R/2L)t
q = 1mC · e
cos
t+ϕ
−
LC
4L2
(a) What is the angular frequency ω 0 of the circuit ? ( hint: how to read out the period T ? T =
(b) What is the inductance L? (hint: the amplitude drops as e−(
)t
(c) With the values of ω 0 , R and L, what is the capacitance C? (C =
)
)
)
(d) What is the phase ϕ? (hint: consider t = 0s)
(e) If removing R, what is the angular frequency ω0 of the circuit ? (hint: the new circuit is a
)
circuit.
(f) If we connect this L-R-C circuit to a AC source, what is the angular frequency of the source that
makes the current amplitude maximum ? (this frequency is known as resonance frequency)
recall for AC L-R-C series circuit, the current amplitude,
V
I=q
R2 + ωL −
1 2
ωC
.
keys: (a) T = 1s =⇒ ω 0 = 2π rad/s (b) L = 0.346574 H (c) C = 0.458527 F (d) ϕ = 0 (e) L-C circuit,
1
1
so ω0 = LC
= 39.5985 rad/s (f) resonance frequency ω = LC
= 39.5985 rad/s
1