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Physics 21
Fall, 2004
Solution to HW17
30
P15
Ignoring any mutual inductance, what is the
equivalent inductance of two inductors connected (a) in se
ries, (b) in parallel?
(a) The same current
I
ﬂows through two inductors in series,
and the voltage across the two inductors is
E
=
E
2
+
E
2
=
−
L
1
dI
dt
+
−
L
2
dI
dt
=
−
(
L
1
+
L
2
)
dI
dt
,
so the inductance is
L
=
L
1
+
L
2
.
(b) For two inductors in parallel, the current
I
splits into
I
1
and
I
2
, and the voltages across the two inductors are equal:
E
=
E
1
=
E
2
=
−
L
1
dI
1
dt
=
−
L
2
dI
2
dt
.
We can write
E
=
−
L
dI
dt
=
−
L
µ
dI
1
dt
+
dI
2
dt
¶
.
Using
dI
1
/dt
=
−E
/L
1
and
dI
2
/dt
=
−E
/L
2
, we see that
E
=
L
(
E
/L
1
+
E
/L
2
)
⇒
1
L
=
1
L
1
+
1
L
2
.
30
P20
What is the energy density at the center of a cir
cular loop of wire carrying a 30 A current if the radius of
the loop is 28 cm?
The magnetic ±eld at the center of a loop of radius
R
carrying current
I
is
B
=
µ
0
I/
2
R
, so the energy density is
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This note was uploaded on 08/06/2008 for the course PHYS 21 taught by Professor Hickman during the Fall '07 term at Lehigh University .
 Fall '07
 Hickman
 Physics, Current, Energy, Power

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