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8B Worksheet Answers
7. DC Circuits
1. Series Circuit
a)
b)
I
batt
=
I
1
=
I
2
c)
V
batt
=
V
1
+
V
2
d)
P
batt
=
P
1
+
P
2
e)
P
batt
=
I
batt
V
batt
=
I
batt
V
1
+
I
batt
V
2
=
I
1
V
1
=
I
2
V
2
=
I
1
2
R
1
+
I
2
2
R
2
=
P
1
+
P
2
R
eff
= 18
Ω
I
batt
= 5 / 9 A
P
1
=
I
1
2
R
1
= 50 / 27 W
P
2
=
I
2
2
R
2
= 100 / 27 W
P
1
+
P
2
= 50 / 9 W
P
batt
=
I
batt
V
batt
= 50 / 9 W = 5.556 W
Parallel Circuit
a)
b)
I
batt
=
I
1
+
I
2
c)
V
batt
=
V
1
=
V
2
d)
P
batt
=
P
1
+
P
2
e)
P
batt
=
I
batt
V
batt
=
I
1
V
batt
+
I
2
V
batt
=
I
1
V
1
=
I
2
V
2
=
I
1
2
R
1
+
I
2
2
R
2
=
P
1
+
P
2
R
eff
= 4
Ω
I
batt
= 5 / 2 A
P
1
=
V
1
2
/
R
1
= 50 / 3 W
P
2
=
V
2
2
/
R
2
= 25 / 3 W
P
1
+
P
2
= 25 W
P
batt
=
I
batt
V
batt
= 25 W
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View Full Document 2. Left Circuit
a)
R
eq
= 2
R
I
batt
=
V
batt
/ 2
R
b)
Junction Rules:
I
1
=
I
2
+
I
3
A
Loop Rules:
V
batt

I
2
(4
R
) = 0
a

I
3
R

I
3
(2
R
) 
I
3
R
+
I
2
(4
R
) = 0
b
Solving Equation
b
gives
I
2
=
I
3
b
’
Plugging
b
’ into
A
gives
I
1
= 2
I
2
A
’
Solving
a
gives
I
2
=
V
batt
/ 4
R
a
’
Plugging
a
’ into
A
’, finally, gives
I
1
=
V
batt
/ 2
R
, (which is what we found in part (a)), so
I
1
=
V
batt
/ 2
R
I
2
=
V
batt
/ 4
R
I
3
=
V
batt
/ 4
R
Right Circuit
a)
R
eq
= 15
R
/ 8
I
batt
= 8
V
batt
/ 15
R
b)
Junction Rules:
I
1
=
I
2
+
I
3
A
Loop Rules:
V
batt

I
2
(4
R
) 
I
2
R
= 0
a

I
3
R

I
3
(2
R
) +
I
2
R
+
I
2
(4
R
) = 0
b
Solving Equation
b
gives
I
3
= 5/3
I
2
b
’
Plugging
b
’ into
A
gives
I
1
= 8/3
I
2
A
’
Solving
a
gives
I
2
=
V
batt
/ 5
R
a
’
Plugging
a
’ into
A
’, finally, gives
I
1
= 8
V
batt
/ 15
R
, (which is what we found in part (a)), so
I
1
= 8
V
batt
/ 15
R
I
2
=
V
batt
/ 5
R
I
3
=
V
batt
/ 3
R
3. a) 12 bulbs
b) 8 bulbs
c) The parallel arrangement will result in the lowest effective resistance, and so the
highest current. The power delivered by the battery is
IV
, so a higher current will
result in a greater power, which will drain the battery’s energy fastest.
d)
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This note was uploaded on 10/16/2010 for the course PHYS 8B taught by Professor Catherinebordel during the Spring '10 term at University of California, Berkeley.
 Spring '10
 CatherineBordel
 Physics, Work

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