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32-1
Conceptual Questions
32.1. (a) a: –100 V b: +60 V c: +80 V. The emf is the x-component of the counterclockwise rotating vectors.
(b) a: Decreasing b: Decreasing c: Increasing
32.2. (a) 1.0 A. Use /.
RR
IVR= (b) 4.0 A. Use 0
//.
RR
IVRR
ε
== (c) 2.0 A. R
I does not depend on frequency.
32.3. (a) 4.0 A. Use 0c
IC
ωε
= for all parts of this question. (b) 4.0 A (c) 4.0 A
32.4. (a) 100 Hz.
c
f= Use 1
2.
cc
f
C
ωπ
== (b) 100 Hz. Use 1
2.
cc
f
C
ωπ
== (c) 200 Hz. The crossover
frequency does not depend on the peak emf.
32.5. (a) 1.0 A.
L
I= Use 0
//()
LLL
IVXL
εω
== for all parts of this question. (b) 4.0 A.
L
I=(c) 1.0 A.
L
I=
32.6. (a) 1000 Hz. Use 0
1.
C
ω
= Resistance does not matter. (b) 11000Hz707.1Hz
2=
(c) 11000Hz707.1Hz
2= (d) 1000 Hz. Peak emf does not matter.
32.7. Less than. Here the current leads the emf, so we know that
φ
< 0 (see Equation 35.22). From Equation 35.27, we find
1
tan001
LCL
LC
C
XXX
XX
RX
φ
−−
⎛⎞
=<⇒−<⇒<
⎜⎟
⎝⎠
The reactances are given by 1/()
c
XC
ω
= and ,
L
XL
ω
= and the resonance frequency is 01/.
C
ω
= Combining
these relationships gives
2
0
1
1
L
C
XLC
XLC
ωωω
=<⇒<=
32.8. We are given that 0.
ωω
< From the last relationship of the analysis in Q32.7, we see that this implies that
,
LC
XX> so
φ
> 0 and the current lags the emf.
32.9. The power will increase when the peak current I increases. This will increase when you (1) decrease R, (2) set
.
LC
XX=
ACCIRCUITS 32