PHY2061
R. D. Field
Solutions
Chapter 31
Page 1 of 6
Chapter 31 Solutions
Problem 1:
How much current passes through the
1
Ω
resistor in the circuit shown in the
Figure
?
Answer:
6I/11
Solution:
Since the potential drop across
each resistor is the same (i.e. parallel) we
know that
3
3
2
2
1
1
R
I
R
I
R
I
=
=
and in addition
I
I
I
I
=
+
+
3
2
1
.
Hence,
I
R
R
R
R
I
R
I
R
R
I
R
I
=
+
+
=
+
+
3
1
2
1
1
3
1
1
2
1
1
1
1
and solving for
I
1
gives
I
I
R
R
R
R
I
I
11
6
3
1
2
1
1
1
3
1
2
1
1
=
+
+
=
+
+
=
r
r
r
A
B
r
r
r
r
r
r
r
r
R
r
cut
Problem 2:
Consider the infinite chain of resistors shown in the
Figure
.
Calculate the
effective resistance,
R
, (
in Ohms
) of the network between the terminals
A
and
B
given that each of the resistors has resistance
r = 1 Ohm
.
2
Ω
1
Ω
3
Ω
I
I
1
I
2
I
3
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PHY2061
R. D. Field
Solutions
Chapter 31
Page 2 of 6
R
1
= 4
Ω
24 V
I
I
2
I
1
R
2
= 12
Ω
R
0
= 3
Ω
Answer:
0.7
Solution:
We first cut
the infinite chain at the
point shown in the
figure and replace the
infinite chain to the
right of the cut by its
effective resistance
R
.
We then combine the
three resistors in series
and then combine
r
and
R+2r
in parallel giving,
r
R
r
R
2
1
1
1
+
+
=
,
which implies that
0
2
2
2
2
=
−
+
r
rR
R
and
(
)
.
73
.
0
3
1
r
r
R
=
+
−
=
Problem 3:
Consider the circuit consisting of an EMF
and three resistors shown in the
Figure
.
How much current flows through the
4
Ω
resistor (
in Amps
)?
Answer:
3
Solution:
The original circuit is equivalent
to a circuit with and EMF and one resistor with resistance
R
tot
given by
Ω
=
Ω
+
Ω
=
+
Ω
=
6
3
3
3
eff
tot
R
R
,
where
R
eff
= 3
Ω
from
Ω
=
Ω
+
Ω
=
3
1
12
1
4
1
1
eff
R
.
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 Spring '08
 FRY
 Physics, Current, Energy, Resistor, Electrical impedance, Series and parallel circuits

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