What is the inductive reactance of a circuit with an inductor of 20 mH at 60 cycles?

What is the inductive reactance of a circuit with an inductor of 20 mH at 60 cycles?

• A. 5.654 ohms
• B. 7.536 ohms
• C. 10.000 ohms
• D. 12.000 ohms

Answer: (B)

To find the inductive reactance of 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, and \( L \) is the inductance in henries. In this case, you have: - An inductance \( L = 20 \) mH, which is equal to \( 0.020 \) H. - A frequency \( f = 60 \) cycles per second, or 60 Hz. Substituting these values into the formula gives: \[ X_L = 2 \pi (60)(0.020) \] Calculating this: 1. \( 2 \pi = 6.2832 \) 2. Multiply this by the frequency: \( 6.2832 \times 60 = 376.992 \) 3. Finally, multiply by the inductance: \( 376.992 \times 0.020 = 7.53984 \) ohms This value rounds to approximately 7.54 ohms, which corresponds most closely to the answer choice

To find the inductive reactance of 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, and ( L ) is the inductance in henries.

In this case, you have:

• An inductance ( L = 20 ) mH, which is equal to ( 0.020 ) H.

• A frequency ( f = 60 ) cycles per second, or 60 Hz.

Substituting these values into the formula gives:

[

X_L = 2 \pi (60)(0.020)

]

Calculating this:

1. ( 2 \pi = 6.2832 )

2. Multiply this by the frequency:

( 6.2832 \times 60 = 376.992 )

3. Finally, multiply by the inductance:

( 376.992 \times 0.020 = 7.53984 ) ohms

This value rounds to approximately 7.54 ohms, which corresponds most closely to the answer choice