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E=1/2 CV^2 E= 1/2 (164 microF) (10^-6 F) (119 V)^2 E= 1.168 J How do you...

E=1/2 CV^2 E= 1/2 (164 microF) (10^-6 F) (119 V)^2 E= 1.168 J How do you figure out the J from the F V^2

Expert Solution

We begin with dimensional analysis. The formula we have is

Where F = Farads, V = Volts, and J = Joules.

Starting with J which is the unit of both Work and Energy. Work is Force times Distance, i.e.
This gives us the units, ,
N = Newtons and L = length.

On the other side we have C and V². Taking C first, which is given by, Capacitance = Charge divided by Voltage, i.e. , Q = fundamental unit so we can't break it down further.

For V, we have,

Where, epsilon the vacuum permittivity is given by the coulomb force,

Using this in the equation of V, we have,

Now we have what we need, so we can see what units 1/2 CV^2 will have,

genius_generous answered 5 months ago

proof of eulers theory:- V+F-E=2

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