Units of Time Constant are Seconds... But Why?

It is a known fact that time constant of a series circuit is RC that is ohm*farad... But how come the units are seconds? Similarly we also have T=L/R Henry/Ohm...even then the units are seconds... Can someone tell me how the units are arrived at? Please help....

Re: Unists of Time Constant are Seconds... But Why?

let's look at the equations and the units:

C=Q/V
[Farad]=[colomb/volt]

R=V/I
[ohm]=[volt/amper]

I=dQ/dt
[amper]=[colomb/time]

RC=(V/I)*(Q/V) --> [RC]=[volt/amper]*[colomb/volt]

[RC]=[volt*time/colomb]*[colomb/volt]=[time]

And, in a simple way, let's see the other one:

T= L/R

in a coil: V=L(di/dt) or we can just say: V=L(I/t), resulting in: L= [(V)(t)] / I

Ohm's Law: I=V/R then: R= V/I


In the end: L/R = [(V)(t) / I] / (V/I)

..( L ) .. ( V*t ) .. ( I )
..----- = ------- * ------ = t (seconds)
..( R ) ... ( I ) .... ( V )


See ya! 8)

In ancient times (100 years ago) all electrical units were express on the primary units basis:
(centimetre, gram, second) OR (meter,kg, second).
For example the electrical capacity unit was "cm" ,
the resistance unit was "sec" .
The electrical charge unit was (cm ^3/2 gram ^1/2 sec^-1 )
(Isn't it strange? )
Units for current, voltage and other were in form of the multiplication/division (and their fractional powers) of c,g,s primary units.
Time constant was "sec x cm" !

The text was completly rewritten 12-04-2005.
(Without checking I assumed, that unit for time constant would be "sec" in SI and cgs systems, closer analyse gives conclusions described above).

purifier said:

It is a known fact that time constant of a series circuit is RC that is ohm*farad... But how come the units are seconds? Similarly we also have T=L/R Henry/Ohm...even then the units are seconds... Can someone tell me how the units are arrived at? Please help....

Click to expand...

All things are calculated in SI units, and if you check a website about SI units, you can find how all units are derived. There are 7 SI base unites and all other SI units are derived from these and can be expressed in terms of SI base units
Check this site for example: https://physics.nist.gov/cuu/Units/units.html
The 7 SI base units:
Expression in terms of SI base units:
Electrical resitance, R (ohm) [Ω]: m^2 · kg · s^-3 · A^-2
Capacitance, C (farad) [F]: m^-2 · kg^-1 · s^4 · A^2
Inductance, L (henry) [H]: m^2 · kg · s^-2 · A^-2

If you multiply the two SI units for R and C, you will end up with the SI unit seconds:
R·C: (m^2 · kg · s^-3 · A^-2) · (m^-2 · kg^-1 · s^4 · A^2) = s

If you devide the SI unit for L with the SI unit for R, you will also end up with the SI unit seconds:
L/R: (m^2 · kg · s^-2 · A^-2) / (m^2 · kg · s^-3 · A^-2) = s

Whenever you are in doubt which unit you will end up with when you multiply, divide, add or subtract more units, just check the SI units and you will know which unit you will end up with.

Without using matematical equasions, just try to imagine this:
Charge/discharge a capacitor .. How much time you need to discharge/charge it?
The answer is time, and it will be reflected in s, ms, µs so on ..

The time required to charge a capacitor to 63 percent (actually 63.2 percent) of full charge or to discharge it to 37 percent (actually 36.8 percent) of its initial voltage is known as the TIME CONSTANT (TC) of the circuit. Hence the unit for time constant is seconds.

[R]=[V]/

[C]=[Q]/[V]=*[t]/[v]

so [R*C]=[R]*[C]=[t]

Simplifying all messages above:

1 farad = 1 coulomb / 1 volt

1 coulomb = 1 ampere * 1 second

so 1 farad = 1 ampere * 1 second / 1 volt

1 ohm = 1 volt / 1 ampere

multiplying 1 farad and 1 ohm, we have

(1 ampere * 1 second / 1 volt) * (1 volt / 1 ampere)

volts and amperes are cancelled
and
that remains 1 second (only time unit)

Thanks a lot... I never expected that many replies... I guess this time i'll think a little before posting such questions... I wonder why i got such a doubt

the proportions are constant