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

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

• A. 60 Hz
• B. 796 Hz
• C. 1000 Hz
• D. 50 Hz

Answer: (B)

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

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