In a series RLC circuit, if the total impedance is 40 Ω, the resistance is 30 Ω,

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Question: In a series RLC circuit, if the total impedance is 40 Ω, the resistance is 30 Ω, what is the inductive reactance? (2021)

Options:

Correct Answer: 10 Ω

Exam Year: 2021

Solution:

Using Z = √(R² + Xl²), we have 40 = √(30² + Xl²). Solving gives Xl = 10 Ω.

In a series RLC circuit, if the total impedance is 40 Ω, the resistance is 30 Ω, what is the inductive reactance? (2021)

In a series RLC circuit, if the total impedance is 40 Ω, the resistance is 30 Ω, what is the inductive reactance? (2021)

Step 1: Write down the formula for total impedance in a series RLC circuit: Z = √(R² + Xl²).
Step 2: Substitute the known values into the formula. Here, Z = 40 Ω and R = 30 Ω.
Step 3: Set up the equation: 40 = √(30² + Xl²).
Step 4: Square both sides of the equation to eliminate the square root: 40² = 30² + Xl².
Step 5: Calculate 40² and 30²: 1600 = 900 + Xl².
Step 6: Subtract 900 from both sides to isolate Xl²: 1600 - 900 = Xl².
Step 7: Calculate the left side: 700 = Xl².
Step 8: Take the square root of both sides to find Xl: Xl = √700.
Step 9: Simplify √700 to find the inductive reactance: Xl = 10 Ω.

Impedance in RLC Circuits – Understanding the relationship between total impedance, resistance, and inductive reactance in a series RLC circuit.
Pythagorean Theorem in Electrical Engineering – Applying the Pythagorean theorem to calculate unknown values in circuits involving resistive and reactive components.