In an AC circuit, if the resistance is 10 ohms and the inductive reactance is 20

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Question: In an AC circuit, if the resistance is 10 ohms and the inductive reactance is 20 ohms, what is the impedance? (2020)

Options:

Correct Answer: √(10² + 20²)

Exam Year: 2020

Solution:

The impedance Z = √(R² + XL²) = √(10² + 20²) = √(100 + 400) = √500 = 22.36 ohms.

In an AC circuit, if the resistance is 10 ohms and the inductive reactance is 20 ohms, what is the impedance? (2020)

In an AC circuit, if the resistance is 10 ohms and the inductive reactance is 20 ohms, what is the impedance? (2020)

Step 1: Identify the resistance (R) and the inductive reactance (XL) from the problem. Here, R = 10 ohms and XL = 20 ohms.
Step 2: Write down the formula for impedance (Z) in an AC circuit: Z = √(R² + XL²).
Step 3: Substitute the values of R and XL into the formula: Z = √(10² + 20²).
Step 4: Calculate R²: 10² = 100.
Step 5: Calculate XL²: 20² = 400.
Step 6: Add the results from Step 4 and Step 5: 100 + 400 = 500.
Step 7: Take the square root of the sum from Step 6: Z = √500.
Step 8: Calculate the square root: √500 ≈ 22.36.
Step 9: State the final answer: The impedance is approximately 22.36 ohms.

Impedance in AC Circuits – Impedance (Z) is the total opposition to current flow in an AC circuit, calculated using the formula Z = √(R² + XL²), where R is resistance and XL is inductive reactance.