Question

When is the impedance \[Z=\sqrt{R^2+(X_C-X_L)^2}\] minimum?

Options

• \[X_C-X_L=0\]

• \[X_C-X_L=R\]

• \[X_C+X_L=R\]

• \[X_C=X_L+R\]

Answer 1

The squared reactance difference cannot be negative, so it contributes least when it is zero. This gives the resonance condition \[X_C=X_L\].