Re: Don was saying...

From: bok (bok_at_nowhere.invalid)
Date: 01/20/05 

Date: Fri, 21 Jan 2005 11:50:17 +1300

bok wrote:
> Don Lancaster wrote:
>
>> bok wrote:
>>
>>> Don Lancaster wrote:
>>>
>>>> Bok wrote:
>>>>
>>>>> Don said:
>>>>> "The v-i transfer function always applies. Impedance is the
>>>>> instantaneous slope of that function".
>>>>>
>>>>> Mathemetically this can be stated resistance: R = dV / dI .
>>>>>
>>>>> Ohm's law, as stated, is just a specific case of the above were dV
>>>>> / dI
>>>>> remains constant for a (in practice limited) range of voltage and
>>>>> current. Materials where R is constant over a useful range of voltages
>>>>> are sometimes referred to as 'ohmic'.
>>>>>
>>>>> An incandescent light bulb is another example of clearly 'non ohmic'
>>>>> resistance.
>>>>
>>>>
>>>>
>>>> You are confusing "big R" constant with "little r" slope.
>>>
>>>
>>> I'm not confused, but I can see the notation I used might be confusing.
>>>
>>> The "big R" in R = dV / dI is NOT intended to denote a constant, since
>>> the differential term dV / dI (or slope) is only a constant in the
>>> linear case. R is a variable representing a variable resistance.
>>>
>>> I can change the notation to r = dV / dI if that's less confusing. The
>>> concepts, however, remain unchanged.
>
>
>> Not at all. R is a constant r is a variable.
>
>
> Respectfully Don, R and r are upper and lower case letters respectively.
> They could be x and y as long as we explain what we mean in either case.
>
> I don't disagree with your convention to use a lower case r to represent
> a variable resistance. However, this does not make the equation R = dV /
> dI invalid as long as everyone is clear that "R" is a variable and to
> anyone who understands what dV / dI means this is fairly obvious.
>

I guess I shouldn't assume everyone is familiar with differential
calculus and Leibniz notation for infinitessimals. The term dV / dI
represents the derivative of voltage w.r.t. current or the slope of the
transfer function in Don's words. This is only a constant when the
transfer function is a straight line. There is considerable difference
between the statements R = V / I and r = dV / dI. The former is just a
special case of the latter.