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DC Circuits  II
Gustav Robert
Kirchhoff (18241887)
Last Time
Resistors in series add
Kirchhoff’s Laws:
Loop law: conservation of energy
Junction law: conservation of charge
Resistors in parallel
Examples
Voltmeters and ammeters
Today
This lecture: HRW 27.727.8
For next time: HRW 27.9
2
Resistors in Parallel
Resistors in
parallel
have the
same potential across them.
Use Kirchhoff’s Laws to find the
equivalent resistance
.
Kirchhoff’s current law at node a,
A.
i
1
=i
2
+i
3
For the outer loop (clockwise),
C.
E
i
R
=0.
For the left loop (clockwise),
B.
E
Kirchhoff’s voltage law can be applied twice:
We now have
3 equations, 3 unknowns:
,i
Note: we could have chosen the right loop instead of
B
or
C
.
What about node b?
1
R
2
R
E
eq
R
a
a
b
b
=i
,
the same eq.
3
Resistors in Parallel (cont.)
1
=;
R
E
2
=
R
E
From
B
and
C
,
12
=+.
RR
EE
Plug these into
A
,
⎛
⎞
⎜
⎟
⎝
⎠
11
=+
E
Rearranging,
eq
1
2
1
R
and since
eq
1
=
R
E
Ä
For n parallel
resistors,
∑
n
i
eq
i
=
Resistors in parallel add
like capacitors in series.
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 Spring '07
 HUANG,TAIYIN
 Charge, Magnetism, Conservation Of Energy, Energy

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