What is the total impedance of a series AC circuit having a resistance of 6 ohms, an inductive reactance of 17 ohms, and zero capacitive reactance?

What is the total impedance of a series AC circuit having a resistance of 6 ohms, an inductive reactance of 17 ohms, and zero capacitive reactance?

• A. 15 ohms
• B. 27 ohms
• C. 18 ohms
• D. 5 ohms

Answer: (C)

To find the total impedance in a series AC circuit that includes resistance and inductive reactance, you use the formula: Z = √(R² + X_L²), where Z is the total impedance, R is the resistance, and X_L is the inductive reactance. In this case, the resistance (R) is 6 ohms, and the inductive reactance (X_L) is 17 ohms. Plugging these values into the formula, you calculate: Z = √(6² + 17²) = √(36 + 289) = √325 = 18.03 ohms (approximately). This rounds to 18 ohms, making it the correct calculation for total impedance in the circuit. This approach effectively illustrates how resistance adds to reactance in an AC circuit, leading to the total impedance being a combination of these two factors. The inductive reactance creates a phase shift, thereby affecting the overall impedance, but since there is no capacitive reactance present, the calculation remains straightforward with just the resistance and inductive reactance considered. Overall, understanding how to compute total impedance is crucial for evaluating AC circuits in practice.

To find the total impedance in a series AC circuit that includes resistance and inductive reactance, you use the formula:

Z = √(R² + X_L²),

where Z is the total impedance, R is the resistance, and X_L is the inductive reactance.

In this case, the resistance (R) is 6 ohms, and the inductive reactance (X_L) is 17 ohms. Plugging these values into the formula, you calculate:

Z = √(6² + 17²)

= √(36 + 289)

= √325

= 18.03 ohms (approximately).

This rounds to 18 ohms, making it the correct calculation for total impedance in the circuit.

This approach effectively illustrates how resistance adds to reactance in an AC circuit, leading to the total impedance being a combination of these two factors. The inductive reactance creates a phase shift, thereby affecting the overall impedance, but since there is no capacitive reactance present, the calculation remains straightforward with just the resistance and inductive reactance considered. Overall, understanding how to compute total impedance is crucial for evaluating AC circuits in practice.