What is the total impedance of a series AC circuit with an inductive reactance of 24 ohms, a resistance of 16 ohms, and a capacitive reactance of 16 ohms?

What is the total impedance of a series AC circuit with an inductive reactance of 24 ohms, a resistance of 16 ohms, and a capacitive reactance of 16 ohms?

• A. 20 ohms
• B. 16 ohms
• C. 10 ohms
• D. None of the above

Answer: (B)

To find the total impedance in a series AC circuit, you need to consider the contributions from resistance, inductive reactance, and capacitive reactance. In this case, you have a resistance of 16 ohms, an inductive reactance of 24 ohms, and a capacitive reactance of 16 ohms. The formula for total impedance in a series circuit is given by: \[ Z = R + j(X_L - X_C) \] where \( R \) is the resistance, \( X_L \) is the inductive reactance, and \( X_C \) is the capacitive reactance. The reactances are considered in the imaginary component of impedance, where positive values represent inductive reactance and negative values represent capacitive reactance. Substituting the values into the equation gives: - Resistance, \( R = 16 \) ohms - Inductive reactance, \( X_L = 24 \) ohms - Capacitive reactance, \( X_C = 16 \) ohms First, calculate the net reactance: \[ X_L - X_C = 24 - 16 = 8 \] ohms Now, the impedance can be expressed

To find the total impedance in a series AC circuit, you need to consider the contributions from resistance, inductive reactance, and capacitive reactance.

In this case, you have a resistance of 16 ohms, an inductive reactance of 24 ohms, and a capacitive reactance of 16 ohms. The formula for total impedance in a series circuit is given by:

[ Z = R + j(X_L - X_C) ]

where ( R ) is the resistance, ( X_L ) is the inductive reactance, and ( X_C ) is the capacitive reactance. The reactances are considered in the imaginary component of impedance, where positive values represent inductive reactance and negative values represent capacitive reactance.

Substituting the values into the equation gives:

• Resistance, ( R = 16 ) ohms

• Inductive reactance, ( X_L = 24 ) ohms

• Capacitive reactance, ( X_C = 16 ) ohms

First, calculate the net reactance:

[ X_L - X_C = 24 - 16 = 8 ] ohms

Now, the impedance can be expressed