What is the inductive reactance of a 60 cycle circuit with a 39.8 mH inductor, rounded to the nearest whole number?

To determine the inductive reactance of an inductor in a circuit, you can use the formula:

[ X_L = 2 \pi f L ]

where ( X_L ) is the inductive reactance in ohms, ( f ) is the frequency in hertz (Hz), and ( L ) is the inductance in henries (H).

In this case, the frequency given is 60 Hz, and the inductance is 39.8 mH (which is equal to ( 39.8 \times 10^{-3} ) H or 0.0398 H).

Now, substituting the values into the formula:

1. Calculate ( 2 \pi ):

[ 2 \pi \approx 6.2832 ]

2. Multiply ( 2 \pi ) by the frequency:

[ 6.2832 \times 60 \approx 376.992 ]

3. Now, multiply this result by the inductance:

[ 376.992 \times 0.0398 \approx 15 ]

Rounding 15 to the nearest whole number gives us an inductive reactance of approximately 15