A coil has an inductance of 20 mH and the inductive reactance is 100 Ω. What is the line frequency?

To determine the line frequency from the given inductance and inductive reactance, we can use the relationship between inductive reactance (X_L), inductance (L), and frequency (f). The formula for inductive reactance is given by:

[ X_L = 2 \pi f L ]

Where:

• ( X_L ) is the inductive reactance in ohms (Ω),

• ( f ) is the frequency in hertz (Hz),

• ( L ) is the inductance in henries (H).

From the problem, we know:

• The inductance ( L ) is 20 mH, which is equivalent to ( 0.020 ) H.

• The inductive reactance ( X_L ) is 100 Ω.

Rearranging the formula to solve for frequency gives:

[ f = \frac{X_L}{2 \pi L} ]

Substituting the known values into the equation:

[ f = \frac{100}{2 \pi \times 0.020} ]

Now, calculating this:

1. Calculate ( 2 \pi \times 0.020 ):

• ( 2 \pi \approx