Finding capacitance

[Cia]

Hi all, i've got a question - What formula would I use to find the capacitance required in series with a resistance of 100 ohms so that the phase difference of the circuit is 60 degrees when the frequency is 40 Hz.

Much appreciated

 

[MrAl]

Hi Cia,

Do you want to take your output from across the capacitor (voltage) or
across the resistor (voltage), or as the current through the network?

 

[Gary B]

I believe this is correct: C= 1⁄(200Π(tan(60))
Xc= 1⁄2ΠfC and the phase of Z= tan(Xc/R)

 

[MrAl]

Hello again,


If it really is the voltage across the capacitor as output and because 60 degrees
is one of those 'special' phase angles the formula reduces to:

K=F*R*C
where
F is the frequency in Hertz
R is the resistance in ohms
C is the capacitance in Farads
and K is a constant:
K=sqrt(3)/(2*pi) which is approx equal to:0.2756644477

so to solve for R we would get:
R=K/(F*C)

or to solve for C we would get:
C=K/(F*R)

For example:
with C=1000uf, R would come out to about 6.892 ohms.

If C=100uf then R would come out to about 68.92 ohms, and if
C=10uf then R would come out to about 689.2 ohms.

 

[Cia]

Thanks MrAl and Gary B, your answers really helped me out. Have a great christmas!