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What is the formula for calculating total impedance in a series RLC circuit?

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Question: What is the formula for calculating total impedance in a series RLC circuit?

Options:

  1. Z = R + jX
  2. Z = R + j(X_L - X_C)
  3. Z = R + X_L + X_C
  4. Z = R + j(X_C - X_L)

Correct Answer: Z = R + j(X_L - X_C)

Solution: 

In a series RLC circuit, the total impedance (Z) is given by Z = R + j(X_L - X_C), where X_L is the inductive reactance and X_C is the capacitive reactance.

What is the formula for calculating total impedance in a series RLC circuit?

Practice Questions

Q1
What is the formula for calculating total impedance in a series RLC circuit?
  1. Z = R + jX
  2. Z = R + j(X_L - X_C)
  3. Z = R + X_L + X_C
  4. Z = R + j(X_C - X_L)

Questions & Step-by-Step Solutions

What is the formula for calculating total impedance in a series RLC circuit?
Correct Answer: Z = R + j(X_L - X_C)
  • Step 1: Identify the components in the series RLC circuit: a resistor (R), an inductor (L), and a capacitor (C).
  • Step 2: Calculate the inductive reactance (X_L) using the formula X_L = 2 * π * f * L, where f is the frequency in hertz and L is the inductance in henries.
  • Step 3: Calculate the capacitive reactance (X_C) using the formula X_C = 1 / (2 * π * f * C), where C is the capacitance in farads.
  • Step 4: Substitute the values of R, X_L, and X_C into the total impedance formula: Z = R + j(X_L - X_C).
  • Step 5: Simplify the expression to find the total impedance Z, where j represents the imaginary unit.
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