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

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Multiple Choice

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

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

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