One over?? What does 'one over' actually mean?

[Rosslando]

Hi,

What does 'one over' actually mean? I have found that it gives the opposite of something but why do we need the opposite? if certain constituent parts of a formula are related to the thing you want a value for, why do you then need the inverse of it?

For example if you look at the formula for resonant frequency f = 1/ (2*pi*R*C), R and C are the values of the components in the system and 2*pi is used to convert from degrees to radians (also is this correct?), why do we need the inverse of this to find the frequency?????

Thanks

 

[Deleted member 4993]

Hi,

What does 'one over' actually mean? I have found that it gives the opposite of something but why do we need the opposite? if certain constituent parts of a formula are related to the thing you want a value for, why do you then need the inverse of it?

For example if you look at the formula for resonant frequency f = 1/ (2*pi*R*C), R and C are the values of the components in the system and 2*pi is used to convert from degrees to radians (also is this correct?), why do we need the inverse of this to find the frequency?????

Thanks

Do you know the relationship between "frequency" and "period" - in the context of oscillation?

 

[Dr.Peterson]

Hi,

What does 'one over' actually mean? I have found that it gives the opposite of something but why do we need the opposite? if certain constituent parts of a formula are related to the thing you want a value for, why do you then need the inverse of it?

For example if you look at the formula for resonant frequency f = 1/ (2*pi*R*C), R and C are the values of the components in the system and 2*pi is used to convert from degrees to radians (also is this correct?), why do we need the inverse of this to find the frequency?????

Thanks

One over something (that is, its reciprocal or multiplicative inverse) is what you use to solve certain equations. When it is needed, it is in order to get the quantity you want rather than something else.

Here, RC is the time constant of the circuit, which amounts to the time in seconds for one radian of an oscillation. Therefore, 2πRC is the time for one period (seconds per cycle), and 1/(2πRC), the reciprocal, is the frequency (cycles per second). Without the reciprocal, you would have the period instead of the frequency.

 

[mmm4444bot]

… What does 'one over' actually mean? …

Are you asking about reciprocals?

1/x is the reciprocal of x

I have found that it gives the opposite of something but why do we need the opposite?

I'm not sure what you're asking.

-4 is the opposite of 4

1/4 is the reciprocal of 4

if certain constituent parts of a formula are related to the thing you want a value for, why do you then need the inverse of it …

I'm not sure what you're thinking, when you ask about the "inverse" of a "thing".

To convert degree measure to radian measure, we multiply by Pi/180°

 

[topsquark]

Hi,

What does 'one over' actually mean? I have found that it gives the opposite of something but why do we need the opposite? if certain constituent parts of a formula are related to the thing you want a value for, why do you then need the inverse of it?

For example if you look at the formula for resonant frequency f = 1/ (2*pi*R*C), R and C are the values of the components in the system and 2*pi is used to convert from degrees to radians (also is this correct?), why do we need the inverse of this to find the frequency?????

Thanks

In Physics you always wan to check your units. You might find this page to be helpful.

All of these are in MKSA units.

Capacitance is measured in Farads. \(\displaystyle F = \dfrac{A^2 s^4}{kg m^2}\)

Resistance is measure in Ohms. \(\displaystyle \Omega = \dfrac{kg m^2}{A^2 s^3}\)

(There is likely a quicker way to write these to get the answer but I usually try to convert to base units first.)

Thus RC has units of s. Hence \(\displaystyle f = \dfrac{1}{2 \pi RC}\) has units of 1/s.

-Dan

 

[Rosslando]

Thinking of it in terms of frequency and time period have made it easier to understand, thanks.

So am i right to say that the one is relative to whatver you are trying to work out? like in terms of oscillation is the 1 representing a single cycle? i.e.

f = 1/t
frequency = one cycle / time period ... ?

t=1/f
time period = one cycle / frequency.. ?

because if you divide one cycle by the frequency, which is say 3 Hz and that represents 3 cycles in a second the time period would be 1/3 of a second.

also i can understand the idea of a reciprocal but i cant work out what it means in terms of this application.. like i know frequency is cycles per second and time constant is seconds per cycle but these are just definitions of each one not how they relate to each other..

im not sure if any of this makes sense, it is quite late

cheers