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

1. ## 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....

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

let's look at the equations and the units:

C=Q/V

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]

3. ## Re: Units of Time Constant are Seconds... But Why?

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)

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4. ## Re: Units of Time Constant are Seconds... But Why?

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).

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5. ## Re: Units of Time Constant are Seconds... But Why?

Originally Posted by purifier
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....
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: http://physics.nist.gov/cuu/Units/units.html
The 7 SI base units:
Code:
```Base quantity               	Name    	Symbol
length  	                    meter  	 m
mass 	                       kilogram   kg
time 	                       second     s
electric current 	           ampere 	 A
thermodynamic temperature      kelvin 	 K
amount of substance 	        mole 	   mol
luminous intensity 	         candela 	cd```
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.

6. ## Re: Units of Time Constant are Seconds... But Why?

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 ..

7. ## Re: Units of Time Constant are Seconds... But Why?

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.

8. ## Re: Units of Time Constant are Seconds... But Why?

[R]=[V]/[I]

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

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

9. ## Re: Units of Time Constant are Seconds... But Why?

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)

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

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 :)

11. ## Re: Units of Time Constant are Seconds... But Why?

the proportions are constant

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