How would you calculate the inductive reactance of a 53.08 millihenry inductor in a 60 cycle circuit?

How would you calculate the inductive reactance of a 53.08 millihenry inductor in a 60 cycle circuit?

• A. 15 Ohm
• B. 25 Ohm
• C. 20 Ohm
• D. 30 Ohm

Answer: (C)

To calculate the inductive reactance (XL) of an inductor in a circuit, you can use the formula: \[ XL = 2 \pi f L \] where: - \( XL \) 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 problem specifies a frequency of 60 Hz and an inductor value of 53.08 millihenries (which can be converted to henries by dividing by 1000, resulting in 0.05308 H). Plugging the values into the formula: \[ XL = 2 \pi (60) (0.05308) \] Calculating it step by step: 1. Calculate \( 2 \pi \cdot 60 \): \[ 2 \pi \cdot 60 \approx 376.99 \] 2. Now, multiply this by the inductance: \[ XL \approx 376.99 \cdot 0.05308 \approx 20.00 \, \text{Ohm} \] This results in an

To calculate the inductive reactance (XL) of an inductor in a circuit, you can use the formula:

[ XL = 2 \pi f L ]

where:

• ( XL ) 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 problem specifies a frequency of 60 Hz and an inductor value of 53.08 millihenries (which can be converted to henries by dividing by 1000, resulting in 0.05308 H).

Plugging the values into the formula:

[ XL = 2 \pi (60) (0.05308) ]

Calculating it step by step:

1. Calculate ( 2 \pi \cdot 60 ):

[ 2 \pi \cdot 60 \approx 376.99 ]

2. Now, multiply this by the inductance:

[ XL \approx 376.99 \cdot 0.05308 \approx 20.00 , \text{Ohm} ]

This results in an