1 Multiple Choice 10 points When subjected to a sinusoidal voltage, the impedance of an inductor \( Z_{L} \) increases linearly as the frequency of the voltage source increases. decreases inversely proportionally as the frequency of the voltage source increases. is not affected by the frequency of the voltage source. none of these.

To solve this problem, we need to understand how the impedance of an inductor behaves with respect to frequency in a sinusoidal voltage scenario. 1. **Definition of Impedance of an Inductor**: The impedance \( Z_L \) of an inductor is given by the formula: \[ Z_L = j \omega L \] where: - \( j \) is the imaginary unit, - \( \omega \) is the angular frequency of the voltage source, given by \( \omega = 2\pi f \) (with \( f \) being the frequency in hertz), - \( L \) is the inductance in henries. 2. **Behavior with Frequency**: - As the frequency \( f \) increases, the angular frequency \( \omega \) also increases. - Since \( Z_L \) is directly proportional to \( \omega \), it follows that as \( f \) increases, \( Z_L \) increases linearly. 3. **Evaluating the Options**: - **Increases linearly as the frequency of the voltage source increases**: This is true based on the relationship derived above. - **Decreases inversely proportionally as the frequency of the voltage source increases**: This is false; the impedance does not decrease. - **Is not affected by the frequency of the voltage source**: This is false; the impedance is affected by frequency. - **None of these**: This is also false since one of the options is correct. Based on this analysis, the correct answer is: **Increases linearly as the frequency of the voltage source increases.**