Chapt. 33
Alternating Current or AC
253
a) Draw a diagram. In the main circuit branch, there is a current
I
. In the resistor branch,
there is a current
I
1
. In the inductor branch, there is a current
I
2
. In the capacitor branch,
there is a current
I
3
. The currents are considered unknowns in this problem. The other
quantities are considered knowns.
b) Solve for the resistor current
I
1
in terms of the given knowns
E
0
,
ω
,
R
,
L
, and
C
.
No
differentiation or integration symbols should remain in the formula for
I
1
.
What is the
current amplitude and phase angle?
HINT:
Recall that if potential drop across a device is
proportional to cos(
ωt
), then the phase angle
φ
of the current is when current is expressed
in terms of cos(
ωt
−
φ
).
c) Solve for the inductor current
I
2
in terms of the given knowns
E
0
,
ω
,
R
,
L
, and
C
.
No
differentiation or integration symbols should remain in the formula for
I
2
.
What is the
current amplitude and phase angle?
HINT:
Constants of integration vanish because one
can assume that all currents time average to zero.
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 Fall '06
 Buchler
 Physics, Current, Alternating Current, Magnetic Field, Inductor

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