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RL Circuits
- Thread starter EJR5
- Start date
Hello,
Have a look at the following page of our eBook:
http://www.allaboutcircuits.com/vol_2/chpt_3/4.html
Bertus
Have a look at the following page of our eBook:
http://www.allaboutcircuits.com/vol_2/chpt_3/4.html
Bertus
I have looked at this before doesn't give the algebraic expressions I need or the steps to achieve them.
I have an RL circuit that is currently in series so I know z=RS+XS I need to make this into parallel to get RP and Xp. I have the values for R
I have a series RL circuit with a known impedance I need to convert this into a parallel circuit with the same equivalent impedance. I know Z=RS+XS for a series RL circuit and I have the values of RS & XS. I need to find RP & XS I have seen the following equations in textbooks and on the web but need to know the algebraic method that was used to get to these equations:
Rp = (RS²+XS²)/RS
Xp = J(RS²+XS²)/XS
The equivalent resistance of two resistors in parallel (say R1 is in parallel with R2) is:
\(
Requivalent=\frac{R1*R2}{R1+R2}
\)
So. Rs+Xs=z. z is known to you. Rp is given to you.
All you have to do is:
\(
z=\frac{Rp*Xp}{Rp+Xp}
\)
You know z, you know Rp. Solve for Xp.
\(
Requivalent=\frac{R1*R2}{R1+R2}
\)
So. Rs+Xs=z. z is known to you. Rp is given to you.
All you have to do is:
\(
z=\frac{Rp*Xp}{Rp+Xp}
\)
You know z, you know Rp. Solve for Xp.
I know RS and XS need to find RP and XP so I have two unknowns
Then pick any Rp, say 1 kOhm and solve for Xp.
I use admittance to simplify the process:
For the parallel case:
\(G_p=\frac{1}{R_p}-j\frac{1}{X_p}\)
For the series case:
\(G_s=\frac{1}{R_s+jX_s}=\frac{R_s-jX_s}{R_s^2+X_s^2}=\frac{R_s}{R_s^2+X_s^2}-j\frac{X_s}{R_s^2+X_s^2}\)
Clearly, if Gs and Gp are equivalent, then equating real and imaginary components leads to:
Real Part:
\(\frac{1}{R_p}=\frac{R_s}{R_s^2+X_s^2}\)
And
Imaginary part:
\(\frac{1}{X_p}=\frac{X_s}{R_s^2+X_s^2}\)
From which your required resulting equations are readily determined.
For the parallel case:
\(G_p=\frac{1}{R_p}-j\frac{1}{X_p}\)
For the series case:
\(G_s=\frac{1}{R_s+jX_s}=\frac{R_s-jX_s}{R_s^2+X_s^2}=\frac{R_s}{R_s^2+X_s^2}-j\frac{X_s}{R_s^2+X_s^2}\)
Clearly, if Gs and Gp are equivalent, then equating real and imaginary components leads to:
Real Part:
\(\frac{1}{R_p}=\frac{R_s}{R_s^2+X_s^2}\)
And
Imaginary part:
\(\frac{1}{X_p}=\frac{X_s}{R_s^2+X_s^2}\)
From which your required resulting equations are readily determined.
Part of the problem likely stems from the fact that Z does NOT equal RS+XS, assuming the XS is the reactance of the inductor.
Is it safe to assume that you are not familiar with complex impedance, but are rather working only with reactance? If so, then what you need to do is find the expressions for the magnitude of the impedance for the series circuit and the phase angle of the impedance for the series circuit. The do the same for the parallel circuit. Once you have those expressions, set the two magnitude equations equal to each other and set the two angle equations equal to each other. That will give you your two equations in two unknowns.
