ECH 152A, Fall 2010, Roland Faller
Solution for Homework 1, October 1, 2011
Problem 1
UNITS
Electric current
is the fundamental SI dimension with unit
Ampere
.
For the following quantities combine fundamental SI units to obtain derived SI
units
Electric power, electric charge, resistance, and voltage.
Solution
Power
P
=
U
×
I
→
[
P
] = W = VA =
J
C
C
s
=
J
s
=
kgm
2
s
3
Charge
Q
=
I
s
→
[
Q
] = C = As
Resistance
R
=
U
I
→
[
R
] = Ω =
V
A
=
J
CA
=
kgm
2
A
2
s
3
Voltage
U
=
J
Q
→
[
U
] = V =
J
C
=
kgm
2
As
3
Problem 2
A mercury manometer at 25
◦
C gives a reading of 71.38 cm at a point
where the local acceleration of gravity is 9.82 ms

2
. The atmospheric pressure
is 100.78 kPa. What is the absolute pressure being measured? (
ρ
Hg
(25C) =
13
.
534 gcm

3
. How does it change with the local acceleration of gravity?
Solution
The pressure measured in the manometer corresponds to
p
=
ρgh
= 13
.
534gcm

3
9
.
82ms

2
71
.
38cm
= 13
.
534
×
9
.
82
×
71
.
38
×
10
3
kgm

3
ms

2
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 Fall '09
 Faller
 Fundamental SI Units, local acceleration, fundamental SI dimension, fundamental SI

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