What is the impedance of a circuit with 50 ohms of resistance in series with 30 ohms of inductive reactance?

What is the impedance of a circuit with 50 ohms of resistance in series with 30 ohms of inductive reactance?

• A. 70 ohm
• B. 50 ohm
• C. 58 ohm
• D. 60 ohm

Answer: (C)

To determine the impedance of a circuit that has resistance and inductive reactance in series, you need to use the formula for calculating impedance, which takes into account both resistance and reactance. The formula for the impedance \( Z \) in a series circuit is given by: \[ Z = \sqrt{R^2 + X_L^2} \] where \( R \) is the resistance, and \( X_L \) is the inductive reactance. In this case, the resistance \( R \) is 50 ohms, and the inductive reactance \( X_L \) is 30 ohms. Plugging these values into the formula gives: \[ Z = \sqrt{50^2 + 30^2} \] \[ Z = \sqrt{2500 + 900} \] \[ Z = \sqrt{3400} \] \[ Z \approx 58.31 \text{ ohms} \] Therefore, when rounded to the nearest whole number, the impedance is approximately 58 ohms. This provides a clear understanding of how impedance combines both the resistive and reactive components of the circuit, resulting in the correct choice, which is 58 ohms.

To determine the impedance of a circuit that has resistance and inductive reactance in series, you need to use the formula for calculating impedance, which takes into account both resistance and reactance. The formula for the impedance ( Z ) in a series circuit is given by:

[ Z = \sqrt{R^2 + X_L^2} ]

where ( R ) is the resistance, and ( X_L ) is the inductive reactance.

In this case, the resistance ( R ) is 50 ohms, and the inductive reactance ( X_L ) is 30 ohms. Plugging these values into the formula gives:

[ Z = \sqrt{50^2 + 30^2} ]

[ Z = \sqrt{2500 + 900} ]

[ Z = \sqrt{3400} ]

[ Z \approx 58.31 \text{ ohms} ]

Therefore, when rounded to the nearest whole number, the impedance is approximately 58 ohms. This provides a clear understanding of how impedance combines both the resistive and reactive components of the circuit, resulting in the correct choice, which is 58 ohms.