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# Units of electricity

Original poster: Jared E Dwarshuis <jdwarshui@xxxxxxxxx>

Hi Jared,

Didn't Tesla himself use the old mechanical analogies for tuned
circuit, i.e. likening them to a mass on spring with
friction,  referring to things like impedance as inertia, or am i
mistaken here?  I have often noted the similarities between
mechanical and electrical systems.  Take for example the energy
stored in a capacitor E=1/2CV^2  (c=capacitance, v=voltage) and then
look at the energy in a moving object E=1/2MV^2 (m=mass,
v=velocity).  I agree with you, but it would be nice to see these
things worked out from first principles.

Thanks

Chris R

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Hi Chris:

I Don?t know much about Tesla, just the stuff in biographies.

The energy stored in a capacitor, ½ CVsqrd comes out as:

E = ½ ss/m (As/m)sqrd x (kg m /ss)sqrd x ( m/As)sqrd

The (As/m)sqrd and (m/As)sqrd cancel leaving:

Energy =  kg mm/ss

E = ½ L Isqrd  also works the same way.

You really want to group inductance with kinetic energy and
capacitance with potential energy. So capacitance is associated with ½
k Xsqrd and inductance is associated with ½ M Vel.sqrd (inductors work
by having charge in motion!)

Voltage is in units of joules/coulomb so we can write:

V =Force x (meters/ coulombs)

Since a coulomb is an amp second we can write:

V = Force x (m/As)

q is in coulombs so we can write q = As :

We certainly can multiply meters by both the numerator and denominator
such that  q = m ( As/m)

Now we can write current as  m/s x (As/m) and we can write dI/dt as:
m/ss x (As/m)

Since V = -L dI/dt we are guaranteed that inductance can be written as:

L = kg x (m/As)sqrd

Now lets write V = -L di/dt

[Force] x (m/As) = [kg] x (m/As)sqrd x  [m/ss] x (As/m)

After canceling units of (m/As) on both sides. We get:

Force = Mass x Acceleration

Sincerely: Jared Dwarshuis