Question

For a series RLC circuit, the impedance locus is plotted in the complex plane, the impedance circle is at

• A. \((X_L,0)\)
• B. \((R,0)\)
• C. \((X,0)\)
• D. \((0,0)\)

Hint:

For a series RLC circuit, \[ \boxed{Z=R+j(X_L-X_C)} \] where the resistance \(R\) is constant and only the reactance changes.

Answer 1

The Correct Option is B

Step 1: Write the impedance of a series RLC circuit. The impedance is \[ Z=R+j(X_L-X_C). \] Its real part is \[ \Re(Z)=R, \] which remains constant.

Step 2: Locate the impedance in the complex plane. Since the real part is fixed at \(R\), the impedance locus lies on the line \[ \boxed{\Re(Z)=R.} \] Hence, the impedance locus is centered at \[ \boxed{(R,0).} \] Therefore, \[ \boxed{(B)} \] is the correct answer.