In an RLC series circuit, if the total impedance is 20Ω and the resistance is 15

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Question: In an RLC series circuit, if the total impedance is 20Ω and the resistance is 15Ω, what is the reactance? (2022)

Options:

Correct Answer: 5Ω

Exam Year: 2022

Solution:

Using Z = √(R² + X²), we find X = √(Z² - R²). Here, Z = 20Ω, R = 15Ω.

In an RLC series circuit, if the total impedance is 20Ω and the resistance is 15Ω, what is the reactance? (2022)

In an RLC series circuit, if the total impedance is 20Ω and the resistance is 15Ω, what is the reactance? (2022)

Step 1: Identify the given values. The total impedance (Z) is 20Ω and the resistance (R) is 15Ω.
Step 2: Write down the formula for impedance in an RLC circuit: Z = √(R² + X²).
Step 3: Rearrange the formula to solve for reactance (X): X = √(Z² - R²).
Step 4: Substitute the values into the formula: X = √(20² - 15²).
Step 5: Calculate 20², which is 400.
Step 6: Calculate 15², which is 225.
Step 7: Subtract 225 from 400: 400 - 225 = 175.
Step 8: Take the square root of 175 to find X: X = √175.
Step 9: Simplify √175, which is approximately 13.23Ω.

Impedance in RLC Circuits – Understanding the relationship between total impedance (Z), resistance (R), and reactance (X) in an RLC series circuit.
Pythagorean Theorem in Electrical Engineering – Applying the Pythagorean theorem to calculate reactance from impedance and resistance.