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

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