Ciarán Mc Ardle www.mathsandcomedy.com Ohm’s Law & Expressing Algebra in English. Ohm's Law expresses the relationship that exists between Electromotive Force; Intensity and Resistance. E=IR It states that Electromotive Force is equal to Intensity multiplied by Resistance. We can state, then, that Ohm’s law is expressed by way of an equation. This equation is algebra in the sense that it uses symbols to represent varying magnitudes of Voltage, Amperage and Resistance. It uses the operator: ¿ so as to imply a state of equality between the magnitudes of Voltage, Amperage and Resistance. It is the use of the sign of equality: ¿ that makes Ohm’s Law an equation. Algebraic Symbols and What they Stand For: Symbol Stands Also A 1 | Page
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Ciarán Mc Ardle www.mathsandcomedy.com
Ohm’s Law & Expressing Algebra in English.Ohm's Law expresses the relationship that exists between Electromotive Force; Intensity and Resistance.
E=IR
It states that Electromotive Force is equal to Intensity multiplied by Resistance.
We can state, then, that Ohm’s law is expressed by way of an equation.
This equation is algebra in the sense that it uses symbols to represent varying magnitudes of Voltage, Amperage and Resistance. It uses the operator:
¿
so as to imply a state of equality between the magnitudes of Voltage, Amperage and Resistance.
It is the use of the sign of equality:
¿
that makes Ohm’s Law an equation.
Algebraic Symbols and What they Stand For:Symbol Name:
Stands For: Also Known As:
A Variable Quantity of:
E Electromotive Force
Voltage. Volts.
I Intensity Current; Amperage.
Amps;Amperes.
R Resistance n/a Ohms;Ω.
We can express this relationship with English Words prior to our putting it forth in formula.
This is an excellent practice recommended by my 1st-year Mathematics Textbook, Text and Tests 1. Unless you can express the symbols of a formula in English, you do not understand the formula!
The same holds true for equations.
I :We can phrase the equation:
x=x
AS:
A thing is equal to the same thing.
OR:
A thing is equal - in quantity or magnitude, etc. - to the quantity or magnitude of the same thing.
OR:
A thing is equal - in quantity or magnitude, etc. - to the quantity or magnitude of an identical thing.
II :We can phrase the equation:
x+ y=x
AS:
A thing plus a different thing is equal to the former thing. [y must equal zero.] [The latter thing must equal zero.]
OR:
The quantity or magnitude of a thing plus the quantity or magnitude of another thing is equal to the quantity or magnitude of the former thing. [The quantity, or magnitude, of y must equal zero.] [The quantity or magnitude of the latter thing must equal zero.]
The quantity or magnitude of a thing plus the quantity or magnitude of another thing is equal to the quantity or magnitude of a thing identical - in quantity, or magnitude - to the former thing. [The quantity, or magnitude, of y must equal zero.] [The quantity or magnitude of the latter thing must equal zero.]
III :
We may phrase the equation:
x+ y= y
AS:
A thing plus a different thing is equal to the latter thing. [x must equal zero.] The former thing must equal zero.]
OR:
The quantity or magnitude of a thing plus the quantity or magnitude of a different thing is equal to the quantity or magnitude of the latter thing. [ The quantity or magnitude of x must equal zero.] [The quantity or magnitude of the former thing must equal zero.]
OR:
The quantity or magnitude of a thing plus the quantity or magnitude of a different thing is equal to the quantity or magnitude of a thing identical - in quantity or magnitude - to the quantity or magnitude of the latter thing. [The quantity or magnitude of x must equal zero.] [The quantity or magnitude of the former thing must equal zero.]
A thing plus another thing is equal to a thing different to both the former thing and the latter thing.
OR:
A quantity or magnitude plus another quantity or magnitude is equal to a quantity or magnitude different to the former quantity or magnitude and the latter quantity or magnitude.
OR:
The quantity or magnitude of a thing plus the quantity or magnitude of another thing is equal to the quantity, or magnitude, of a thing different - in quantity or magnitude - to both the quantity or magnitude of the former thing and the quantity or magnitude of the latter thing.
---
Which is easier to Say:
x+ y=z
or the long-winded paragraph above? The signs and symbols of algebra serve as an excellent shorthand!
According to a program that I listened to on B.B.C. Radio 4, Bertrand Russel's book, Principia Mathematica1 concerns rendering simple - but then progressively more difficult! - algebraic equations in English so as to describe and prove the logic of said equations. It is said that Bertrand Russel's Principia Mathematica is a book notoriously difficult to comprehend, but I would like to
1 ‘prīncipium, prīncipiī,’ neuter, 2nd-declension Latin noun, ‘beginning.’ ‘Prīncipia,’ nominative plural, ‘beginnings.’ ‘mathēmaticus, mathēmatica, mathēmaticum,’ 1st-and-2nd-declension adjective, ‘mathematic,’ ‘mathematical.’ ‘mathēmatica,’ nominative neuter plural form of the adjective, agreeing in case, gender and number with ‘Prīncipia.’ Hence, a good translation of ‘Prīncipia Mathēmatica’ would be ‘Mathematical Beginnings.’
The magnitude of Electromotive Force – measured in volts – is equal to the magnitude of Intensity, or Current – measured in amperes – multiplied by the magnitude of Resistance – measured in ohms.
The above formula is easily remembered by way of this mnemonic: think of Eirtricity, an Irish Electricity provider. The first three letters of its name, eir-tricity, spells out ohms law.
We can manipulate the formula for Ohm’s Law so as to make Intensity the subject of the formula:
E=IR
E( 1R )=IR( 1
R )E( 1
R )=I R( 1R )
E( 1R )=I (1 )
E( 1R )=I
ER
=I
I= ER
So, the formula for Ohm’s Law, rewritten so as to make Intensity, or Current, the subject of the equation is:
I= ER
WHICH IN ENGLISH IS:
The magnitude of Intensity, or Current – measured in amperes – is equal to the magnitude of Electromotive Force – measured in volts – divided by the magnitude of Resistance – measured in ohms.
We can – again – manipulate the formula for Ohm’s Law so as to make Resistance the subject of the formula:
E=IR
E( 1I )=IR( 1
I )E( 1
I )=I R( 1I )
E( 1I )=R (1 )
E( 1I )=R
EI=R
R=EI
WHICH IN ENGLISH IS:
The magnitude of Resistance – measured in ohms – is equal to the magnitude of Electromotive Force – measured in volts – divided by the magnitude of Intensity, or Current – measured in amperes.
Note:
The name of the Electricity Provider, mentioned above, is actually Airtricity, but I did not know this prior to my researching this article. However, thinking of Eirtricity as in Electricity Éire has done me great service in remembering Ohm’s Law. A mnemonic is not rendered useless by mere facts!
noun. [mass noun] the part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations.
A system of algebra based on given axioms.
<DERIVATIVES> algebraist /aldʒɪ'breɪɪst/ noun.
<ORIGIN> late Middle English: from Italian, Spanish and medieval Latin, from Arabic al-jabr ‘the reunion of broken parts’, ‘bone-setting’, from jabara ‘reunite, restore’. The original sense, ‘the surgical treatment of fractures’, probably came via Spanish, in which it survives; the mathematical sense comes from the title of a book, ‘ilm al-jabr wa’l-muqābala ‘the science of restoring what is missing and equating like with like’, by the mathematician al-kwārizmi (see ALGORITHM).
amperage /'amp(ǝ)rɪdʒ/
noun.
the strength of an electric current in amperes.
equation /ɪ'kweɪʒ(ǝ)n/
noun. [MATHEMATICS] a statement that the values of two
mathematical expressions are equal (indicated by the sign =).<ORIGIN> late Middle English: from Latin aequatio(n-), from aequare ‘make equal,’ ‘see EQUATE.’
Etmyology: The term equation comes from the Latin 1st and 2nd declension adjective, ‘aequus, aequa, aequum,’ ‘equal;’ and the 3rd-declension termination ‘-tiō’ which denotes a state of being, in this instance a state of being
noun. [Mathematics.] a process in which a number, quantity, expression, etc., is altered or manipulated according to set formal rules, such as those of addition, multiplication, and differentiation.
<ORIGIN> late Middle English: via Old French from Latin operatio(n-), from the verb operari ‘expend labour on’ (see OPERATE).
operator
noun. [MATHEMATICS] a symbol or function denoting an operation (e.g. x, +).
The above definitions are from:
Oxford University Press. Oxford Dictionary of English (Electronic Edition). Oxford. 2010
