What is the mathematical reasoning as to why an AC capacitive voltage divider ratio is inversed (RATIO=C2/C1) and a resistive divider ratio is not (RATIO=R1/R2)? Thanks.
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Thanks for the response. However, why is the impedance of a capacitor inversely proportional to its value?The impedance of a resistor is proportional its value. The impedance of a capacitor is inversely proportional to its value.
Resistance, capacitance, and inductance are all just proportionality constants in the constitutive equations for those three components. As such, the constant could have been put on either side of the equation. It's all in how they are defined.Thanks for the response. However, why is the impedance of a capacitor inversely proportional to its value?
Oddly enough, there actually is a name for that: elastance, the reciprocal of capacitance. Its unit of measurement is the daraf.Similarly, if they had defined capacitance (using a different name, most likely) as a constant on the same side of the equation as Q, then the capacitive voltage divider would have the same form as the resistive one.
Interesting -- I've never run across that, but it doesn't surprise me at all. I can definitely see the line of reasoning as elasticity is the inverse of compliance and capacitance is very analogous to compliance.Oddly enough, there actually is a name for that: elastance, the reciprocal of capacitance. Its unit of measurement is the daraf.
I actually made use of elastance years ago while working on signal conditioning circuitry for a particular class of moving-plate differential-capacitor displacement sensors; expressing the value of the capacitors formed by the parallel plates in terms of elastance, rather than capacitance, gave me a quantity that varied in direct proportion to the separation between the plates, instead of inversely proportional. Since the circuits were designed to output a voltage that varied directly with plate separation, working in darafs (actually teradarafs, given the small size of the plates) made life a lot easier.I've actually used "darafs" before, but I just made it up in class on the fly to show how we can make units up to get them out of the denominator if it makes our lives easier and that, just like the "mho" is reciprocal ohms, we could define the "daraf" to be reciprocal farads and the "yrneh" to be reciprocal henries.
It's actually not as bad when spoken as it is when written. You just imagine some guy from some obscure country being immortalized for their contribution and it suddenly becomes not as bad as some of the other units we've gotten saddled with.I actually made use of elastance years ago while working on signal conditioning circuitry for a particular class of moving-plate differential-capacitor displacement sensors; expressing the value of the capacitors formed by the parallel plates in terms of elastance, rather than capacitance, gave me a quantity that varied in direct proportion to the separation between the plates, instead of inversely proportional. Since the circuits were designed to output a voltage that varied directly with plate separation, working in darafs (actually teradarafs, given the small size of the plates) made life a lot easier.
"Yrneh," however is just... just... just wrong. It's unnatural. It should be outlawed.
I think there are several reasons for this. The obvious one is that they really like naming units to honor people (I suspect they'd love to rename the meter, the gram, and the second if they thought they could get away with it). But there are some practical issues as well. There are many languages (such as Chinese) in which the notion of "spell the unit backwards" just has no meaning.Hi,
Yeah and it is interesting that the unit "mho" is deprecated now although it is still used. Most modern stuff uses Siemens now.