What is the formula for the total impedance in a series RLC circuit? (2023)

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Question: What is the formula for the total impedance in a series RLC circuit? (2023)

Options:

Correct Answer: Z = R + j(XL - XC)

Exam Year: 2023

Solution:

The total impedance in a series RLC circuit is given by Z = R + j(XL - XC).

What is the formula for the total impedance in a series RLC circuit? (2023)

What is the formula for the total impedance in a series RLC circuit? (2023)

Step 1: Identify the components in the series RLC circuit: a resistor (R), an inductor (L), and a capacitor (C).
Step 2: Understand that impedance (Z) is a measure of how much the circuit resists the flow of electric current.
Step 3: Recognize that the total impedance in a series circuit is the sum of the resistance and the reactance.
Step 4: Calculate the inductive reactance (XL) using the formula XL = 2πfL, where f is the frequency and L is the inductance.
Step 5: Calculate the capacitive reactance (XC) using the formula XC = 1/(2πfC), where C is the capacitance.
Step 6: Substitute the values of R, XL, and XC into the formula for total impedance: Z = R + j(XL - XC).
Step 7: Understand that 'j' represents the imaginary unit, which is used to express the phase difference in AC circuits.

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