(a)
Ohm’s Law
Definition: The law that the
direct current flowing in an electric circuit is directly proportional to the
voltage applied to the circuit; it is valid for metallic circuits and many
circuits containing an electrolytic resistance. This law assumes linearity in the lumped EM circuit analysis,
which is a special, but common case for doing ballpark calculations.
When
the current in a conductor is constant and there are no emfs (electromagnetic
forces) within the conductor, the value of the voltage Vbetween the terminals of the conductor is proportional to
the current I, or
V = R X I equation IV a
where
the coefficient of proportionality R is referred to as the
resistance of the conductor.
An
easy way to remember this is using the following picture
Figure 1
So
now you can calculate voltage (V = I x R), current (I = V ¸
R), and resistance
(R = V ¸
I) of a material by following the placement of the electrical characters in the
above diagram of Ohm's Law.
EXAMPLE
If
an operator is wearing a grounded wrist strap with a 1 Megohm resistor in
series to ground and touches an equipment chassis that is at 120 Volts rms AC
with his opposite hand then how much current will travel through the
operator? Is it safe?
Using
Ohm's Law, the current would be (120 V)/(1 MW
) = 0.12 mA. For
safety, UL recommends that the maximum current delivered to a human be limited
to less than 0.25 mA, therefor the current of 0.12 mA is well below the maximum
suggested current and is safe.
(b)
Capacitance and charge storage
Capacitance
is defined as the ratio of the charge on one of the conductors of a capacitor
(there being an equal and opposite charge on the other conductor) to the
potential difference between the conductors.
Symbolized by C. Formerly known
as capacity.
PARALLEL CAPACITOR MODEL
The
capacitance (C in Farads) is equal to the magnitude of the charge (Q in
coulombs) on either body (or plate where Q_{1} = Q_{2} = Q) divided
by the potential (V in Volts) between them.
C
= Q ¸
V (Farads)
equation IV b
The
capacitance in Figure 1 can be approximated by two flat parallel conductors
separated by dielectric of width x where A is the area of either conductors, K is the dielectric
constant of the dielectric separating the two conductors and e
_{o} is the permittivity of free space (e
_{o} = 8.85 x 10^{12} F/m).
C
= (e
_{o} K A) ¸
x
equation IV c
EXAMPLE
What
is the capacitance of a big guy wearing size 13 shoes with 1cm thick soles
having a dielectric constant of 7.3 and both of his feet are on the floor?
Using
equation IV, C = (e
_{o} K A)/x =
(8.85x10^{12}*7.3*0.0464)/0.01,and substituting in the appropriate variable, then his
approximate Capacitance is 300x10^{12} F or 300 pF.
Reference Information:
Commonly
Used Prefixes 

FACTOR 
PREFIX 
SYMBOL 
10^{12} 
tera 
T 
10^{9} 
giga 
G 
10^{6} 
mega 
M 
10^{3} 
kilo 
k 
10^{3} 
milli 
m 
10^{6} 
micro 
m

10^{12} 
pico 
p 
Useful
Physical Units 

QUANTITY 
NAME 
SYMBOL 
EXPRESSION 
force 
newton 
N 
kg·
m·
s^{2} 
time 
second 
s 
s 
electric charge 
coulomb 
Q 
A·
s 
energy 
joule 
J 
N·
m 
power 
watt 
W 
J/s 
electric field
strength 

E 
N/C or V/m 
voltage potential 
volt 
V 
J/C 
capacitance 
farad 
F 
Q/V 
resistance 
ohm 
W

V/A 
volume resistivity 
rho v 
r
_{v} 
W
·
m 
surface resistivity 
rho s 
r
_{s} 
W
/ÿ
