III.    ESD Mathematics

 

(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

Ohm's Law
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


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 Q1 = Q2 = 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

1012

tera

T

109

giga

G

106

mega

M

103

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 /˙