Multiple Choice 10 points At a frequency of 2200 Hz , the impedance of an inductor is measured to be 73.8 ohms, and the DC resistance of the inductor is 26 ohms. What is the expected phase difference between the voltage and current through the inductor? \( 69^{\circ} \) \( 90^{\circ} \) \( 21^{\circ} \) \( 0^{\circ} \) \( 120^{\circ} \)

To find the expected phase difference between the voltage and current through the inductor, we can use the formula for the phase angle \(\phi\): \[ \tan(\phi) = \frac{X_L}{R} \] where \(X_L\) is the inductive reactance and \(R\) is the resistance. The impedance \(Z\) is given by: \[ Z = \sqrt{R^2 + X_L^2} \] We know that: \[ Z = 73.8 \, \text{ohms} \quad \text{and} \quad R = 26 \, \text{ohms} \] To find \(X_L\), we can rearrange the formula: \[ X_L = \sqrt{Z^2 - R^2} = \sqrt{(73.8)^2 - (26)^2} \approx 68.99 \, \text{ohms} \] Now finding the phase angle \(\phi\): \[ \tan(\phi) = \frac{X_L}{R} = \frac{68.99}{26} \approx 2.65 \] \(\phi = \tan^{-1}(2.65) \approx 69^{\circ}\) Thus, the expected phase difference between the voltage and current through the inductor is: \( 69^{\circ} \)