Question

An inductor designed to filter high-frequency noise from power supplied to a personal computer is placed in series with the computer. What minimum inductance should it have to produce a 2.00 kΩ reactance for 15.0 kHz noise?

a) 0.05 H
b) 0.1 H
c) 0.15 H
d) 0.2 H

Answer 1

The minimum inductance required to achieve a reactance of 2.00 kΩ at 15.0 kHz is calculated as 0.0212 H (21.2 mH), which does not match the provided options. The reactance of this inductor at 60 Hz would be approximately 7.96 Ω.

Step-by-step explanation:

To calculate the minimum inductance required for an inductor to have a reactance of 2.00 kΩ at a frequency of 15.0 kHz, we use the formula for inductive reactance, which is X_L = 2πfL, where X_L is the reactance in ohms, f is the frequency in hertz, and L is the inductance in henrys.

Rearranging the formula to solve for L, we get L = X_L / (2πf). Plugging in the values, we have L = 2000 Ω / (2 π × 15000 Hz), which simplifies to an inductor value of 0.0212 H or 21.2 mH. This value is not one of the options provided, so there might be a miscalculation or typo in the provided choices.

For part (b), calculating the reactance at a lower frequency, we use the same formula: X_L = 2πfL. Assuming we use the inductance calculated earlier, X_L = 2π × 60 Hz × 0.0212 H, which gives a reactance of approximately 7.96 Ω at 60 Hz.