In a 100 Hz circuit with a 15 mH inductor, what is the inductive reactance in ohms after converting millihenrys to henrys?

To find the inductive reactance 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,

• ( L ) is the inductance in henrys.

First, we need to convert 15 mH (millihenrys) to henrys:

[ 15 , \text{mH} = 15 \times 10^{-3} , \text{H} = 0.015 , \text{H} ]

Now, substitute the values into the formula. The frequency ( f ) is 100 Hz and the inductance ( L ) is 0.015 H:

[ X_L = 2 \pi (100) (0.015) ]

Calculating this gives:

[ X_L = 2 \pi \cdot 100 \cdot 0.015 ]

[ X_L = 2 \cdot 3.14159 \cdot 100 \cdot 0.015 ]

[ X_L \approx 9.42477