- 10th April 2005, 14:39 #1

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## 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....

- 10th April 2005, 15:05 #2

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## 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]

- 10th April 2005, 15:05

- 11th April 2005, 09:03 #3

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## 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)

- 11th April 2005, 10:21 #4

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## 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).

- 11th April 2005, 10:21

- 11th April 2005, 10:53 #5

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

Originally Posted by**purifier**

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

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.

- 11th April 2005, 10:53

- 11th April 2005, 11:49 #6

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## 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 ..

- 11th April 2005, 12:02 #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.

- 11th April 2005, 12:04 #8

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

[R]=[V]/[I]

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

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

- 11th April 2005, 15:59 #9

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## 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)

- 11th April 2005, 16:26 #10

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## 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 :)

- 11th April 2005, 17:56 #11

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

the proportions are constant