What is the total inductive reactance of a 60-hertz AC circuit with 60 ohms of resistance and 5 henries of inductance?

What is the total inductive reactance of a 60-hertz AC circuit with 60 ohms of resistance and 5 henries of inductance?

• A. 600.00 ohms
• B. 880.00 ohms
• C. 1884.96 ohms
• D. 2400.00 ohms

Answer: (C)

To determine the total inductive reactance in an AC circuit, you can use the formula for inductive reactance, which is given by: \[ X_L = 2\pi f L \] 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, the frequency \( f \) is 60 hertz, and the inductance \( L \) is 5 henries. Plugging these values into the formula, we get: \[ X_L = 2 \pi (60)(5) \] Calculating this step-by-step: 1. Calculate \( 2 \pi \): - Approximately \( 2 \times 3.14159 = 6.28318 \). 2. Multiply this with the frequency and inductance: - \( 6.28318 \times 60 \times 5 \). - First, multiply \( 60 \times 5 = 300 \). - Then, multiply \( 300 \times 6.28318 \approx 1884.96 \)

To determine the total inductive reactance in an AC circuit, you can use the formula for inductive reactance, which is given by:

[ 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, the frequency ( f ) is 60 hertz, and the inductance ( L ) is 5 henries. Plugging these values into the formula, we get:

[ X_L = 2 \pi (60)(5) ]

Calculating this step-by-step:

1. Calculate ( 2 \pi ):

• Approximately ( 2 \times 3.14159 = 6.28318 ).

2. Multiply this with the frequency and inductance:

• ( 6.28318 \times 60 \times 5 ).

• First, multiply ( 60 \times 5 = 300 ).

• Then, multiply ( 300 \times 6.28318 \approx 1884.96 )