In an RLC series circuit, if the total impedance is 50 ohms and the resistance i

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Question: In an RLC series circuit, if the total impedance is 50 ohms and the resistance is 30 ohms, what is the reactance? (2020)

Options:

Correct Answer: 40 ohms

Solution:

Using Z = √(R² + X²), we find X = √(Z² - R²) = √(50² - 30²) = √(2500 - 900) = √1600 = 40 ohms.

In an RLC series circuit, if the total impedance is 50 ohms and the resistance is 30 ohms, what is the reactance? (2020)

In an RLC series circuit, if the total impedance is 50 ohms and the resistance is 30 ohms, what is the reactance? (2020)

Step 1: Identify the given values. The total impedance (Z) is 50 ohms and the resistance (R) is 30 ohms.
Step 2: Write down the formula for impedance in an RLC circuit: Z = √(R² + X²), where X is the reactance.
Step 3: Rearrange the formula to solve for reactance (X): X = √(Z² - R²).
Step 4: Substitute the known values into the formula: X = √(50² - 30²).
Step 5: Calculate 50², which is 2500.
Step 6: Calculate 30², which is 900.
Step 7: Subtract 900 from 2500: 2500 - 900 = 1600.
Step 8: Take the square root of 1600: √1600 = 40.
Step 9: Conclude that the reactance (X) is 40 ohms.

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.