The impedance of an RLC circuit is given by which of the following formulas? (20

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Question: The impedance of an RLC circuit is given by which of the following formulas? (2022)

Options:

Correct Answer: Z = √(R² + (X_L - X_C)²)

Exam Year: 2022

Solution:

The impedance (Z) of an RLC circuit is given by Z = √(R² + (X_L - X_C)²), where X_L is the inductive reactance and X_C is the capacitive reactance.

The impedance of an RLC circuit is given by which of the following formulas? (2022)

The impedance of an RLC circuit is given by which of the following formulas? (2022)

Step 1: Understand that an RLC circuit consists of a resistor (R), an inductor (L), and a capacitor (C).
Step 2: Know that impedance (Z) is a measure of how much the circuit resists the flow of electric current.
Step 3: Identify the components of impedance: resistance (R) and reactance (X).
Step 4: Recognize that the total reactance (X) in an RLC circuit is the difference between inductive reactance (X_L) and capacitive reactance (X_C).
Step 5: Use the formula for impedance: Z = √(R² + (X_L - X_C)²).
Step 6: Remember that X_L is calculated as 2πfL and X_C is calculated as 1/(2πfC), where f is the frequency.

Impedance in RLC Circuits – Impedance is the total opposition that a circuit offers to the flow of alternating current, combining resistance (R) and reactance (X).
Reactance – Reactance is the opposition to alternating current caused by inductors (X_L) and capacitors (X_C), which varies with frequency.
RLC Circuit Components – An RLC circuit consists of a resistor (R), inductor (L), and capacitor (C) connected in series or parallel, affecting the overall impedance.